CSS Ribbon

Reproducing the GitHub Ribbon in CSS

【统计学】第七章

Evernote Export

参数估计的基本原理

一个总体参数的区间估计

两个总体参数的区间估计

样本容量的确定

掌握目标
估计量与估计值的概念
点估计与区间估计的区别
评价估计量优良性的标准
一个总体参数的区间估计方法
两个总体参数的区间估计方法
样本容量的确定方法

<svg id="d9gqnrbh2ac" width="100%" xmlns="http://www.w3.org/2000/svg" style="max-width: 91px;" viewBox="0 0 91 116"><style>


#d9gqnrbh2ac .label {
  font-family: 'trebuchet ms', verdana, arial;
  color: #333; }

#d9gqnrbh2ac .node rect,
#d9gqnrbh2ac .node circle,
#d9gqnrbh2ac .node ellipse,
#d9gqnrbh2ac .node polygon {
  fill: #ECECFF;
  stroke: #9370DB;
  stroke-width: 1px; }

#d9gqnrbh2ac .node.clickable {
  cursor: pointer; }

#d9gqnrbh2ac .arrowheadPath {
  fill: #333333; }

#d9gqnrbh2ac .edgePath .path {
  stroke: #333333;
  stroke-width: 1.5px; }

#d9gqnrbh2ac .edgeLabel {
  background-color: #e8e8e8; }

#d9gqnrbh2ac .cluster rect {
  fill: #ffffde !important;
  stroke: #aaaa33 !important;
  stroke-width: 1px !important; }

#d9gqnrbh2ac .cluster text {
  fill: #333; }

#d9gqnrbh2ac div.mermaidTooltip {
  position: absolute;
  text-align: center;
  max-width: 200px;
  padding: 2px;
  font-family: 'trebuchet ms', verdana, arial;
  font-size: 12px;
  background: #ffffde;
  border: 1px solid #aaaa33;
  border-radius: 2px;
  pointer-events: none;
  z-index: 100; }

#d9gqnrbh2ac .actor {
  stroke: #CCCCFF;
  fill: #ECECFF; }

#d9gqnrbh2ac text.actor {
  fill: black;
  stroke: none; }

#d9gqnrbh2ac .actor-line {
  stroke: grey; }

#d9gqnrbh2ac .messageLine0 {
  stroke-width: 1.5;
  stroke-dasharray: '2 2';
  stroke: #333; }

#d9gqnrbh2ac .messageLine1 {
  stroke-width: 1.5;
  stroke-dasharray: '2 2';
  stroke: #333; }

#d9gqnrbh2ac #arrowhead {
  fill: #333; }

#d9gqnrbh2ac #crosshead path {
  fill: #333 !important;
  stroke: #333 !important; }

#d9gqnrbh2ac .messageText {
  fill: #333;
  stroke: none; }

#d9gqnrbh2ac .labelBox {
  stroke: #CCCCFF;
  fill: #ECECFF; }

#d9gqnrbh2ac .labelText {
  fill: black;
  stroke: none; }

#d9gqnrbh2ac .loopText {
  fill: black;
  stroke: none; }

#d9gqnrbh2ac .loopLine {
  stroke-width: 2;
  stroke-dasharray: '2 2';
  stroke: #CCCCFF; }

#d9gqnrbh2ac .note {
  stroke: #aaaa33;
  fill: #fff5ad; }

#d9gqnrbh2ac .noteText {
  fill: black;
  stroke: none;
  font-family: 'trebuchet ms', verdana, arial;
  font-size: 14px; }

#d9gqnrbh2ac .activation0 {
  fill: #f4f4f4;
  stroke: #666; }

#d9gqnrbh2ac .activation1 {
  fill: #f4f4f4;
  stroke: #666; }

#d9gqnrbh2ac .activation2 {
  fill: #f4f4f4;
  stroke: #666; }


#d9gqnrbh2ac .section {
  stroke: none;
  opacity: 0.2; }

#d9gqnrbh2ac .section0 {
  fill: rgba(102, 102, 255, 0.49); }

#d9gqnrbh2ac .section2 {
  fill: #fff400; }

#d9gqnrbh2ac .section1,
#d9gqnrbh2ac .section3 {
  fill: white;
  opacity: 0.2; }

#d9gqnrbh2ac .sectionTitle0 {
  fill: #333; }

#d9gqnrbh2ac .sectionTitle1 {
  fill: #333; }

#d9gqnrbh2ac .sectionTitle2 {
  fill: #333; }

#d9gqnrbh2ac .sectionTitle3 {
  fill: #333; }

#d9gqnrbh2ac .sectionTitle {
  text-anchor: start;
  font-size: 11px;
  text-height: 14px; }


#d9gqnrbh2ac .grid .tick {
  stroke: lightgrey;
  opacity: 0.3;
  shape-rendering: crispEdges; }

#d9gqnrbh2ac .grid path {
  stroke-width: 0; }


#d9gqnrbh2ac .today {
  fill: none;
  stroke: red;
  stroke-width: 2px; }



#d9gqnrbh2ac .task {
  stroke-width: 2; }

#d9gqnrbh2ac .taskText {
  text-anchor: middle;
  font-size: 11px; }

#d9gqnrbh2ac .taskTextOutsideRight {
  fill: black;
  text-anchor: start;
  font-size: 11px; }

#d9gqnrbh2ac .taskTextOutsideLeft {
  fill: black;
  text-anchor: end;
  font-size: 11px; }


#d9gqnrbh2ac .taskText0,
#d9gqnrbh2ac .taskText1,
#d9gqnrbh2ac .taskText2,
#d9gqnrbh2ac .taskText3 {
  fill: white; }

#d9gqnrbh2ac .task0,
#d9gqnrbh2ac .task1,
#d9gqnrbh2ac .task2,
#d9gqnrbh2ac .task3 {
  fill: #8a90dd;
  stroke: #534fbc; }

#d9gqnrbh2ac .taskTextOutside0,
#d9gqnrbh2ac .taskTextOutside2 {
  fill: black; }

#d9gqnrbh2ac .taskTextOutside1,
#d9gqnrbh2ac .taskTextOutside3 {
  fill: black; }


#d9gqnrbh2ac .active0,
#d9gqnrbh2ac .active1,
#d9gqnrbh2ac .active2,
#d9gqnrbh2ac .active3 {
  fill: #bfc7ff;
  stroke: #534fbc; }

#d9gqnrbh2ac .activeText0,
#d9gqnrbh2ac .activeText1,
#d9gqnrbh2ac .activeText2,
#d9gqnrbh2ac .activeText3 {
  fill: black !important; }


#d9gqnrbh2ac .done0,
#d9gqnrbh2ac .done1,
#d9gqnrbh2ac .done2,
#d9gqnrbh2ac .done3 {
  stroke: grey;
  fill: lightgrey;
  stroke-width: 2; }

#d9gqnrbh2ac .doneText0,
#d9gqnrbh2ac .doneText1,
#d9gqnrbh2ac .doneText2,
#d9gqnrbh2ac .doneText3 {
  fill: black !important; }


#d9gqnrbh2ac .crit0,
#d9gqnrbh2ac .crit1,
#d9gqnrbh2ac .crit2,
#d9gqnrbh2ac .crit3 {
  stroke: #ff8888;
  fill: red;
  stroke-width: 2; }

#d9gqnrbh2ac .activeCrit0,
#d9gqnrbh2ac .activeCrit1,
#d9gqnrbh2ac .activeCrit2,
#d9gqnrbh2ac .activeCrit3 {
  stroke: #ff8888;
  fill: #bfc7ff;
  stroke-width: 2; }

#d9gqnrbh2ac .doneCrit0,
#d9gqnrbh2ac .doneCrit1,
#d9gqnrbh2ac .doneCrit2,
#d9gqnrbh2ac .doneCrit3 {
  stroke: #ff8888;
  fill: lightgrey;
  stroke-width: 2;
  cursor: pointer;
  shape-rendering: crispEdges; }

#d9gqnrbh2ac .doneCritText0,
#d9gqnrbh2ac .doneCritText1,
#d9gqnrbh2ac .doneCritText2,
#d9gqnrbh2ac .doneCritText3 {
  fill: black !important; }

#d9gqnrbh2ac .activeCritText0,
#d9gqnrbh2ac .activeCritText1,
#d9gqnrbh2ac .activeCritText2,
#d9gqnrbh2ac .activeCritText3 {
  fill: black !important; }

#d9gqnrbh2ac .titleText {
  text-anchor: middle;
  font-size: 18px;
  fill: black; }

#d9gqnrbh2ac g.classGroup text {
  fill: #9370DB;
  stroke: none;
  font-family: 'trebuchet ms', verdana, arial;
  font-size: 10px; }

#d9gqnrbh2ac g.classGroup rect {
  fill: #ECECFF;
  stroke: #9370DB; }

#d9gqnrbh2ac g.classGroup line {
  stroke: #9370DB;
  stroke-width: 1; }

#d9gqnrbh2ac .classLabel .box {
  stroke: none;
  stroke-width: 0;
  fill: #ECECFF;
  opacity: 0.5; }

#d9gqnrbh2ac .classLabel .label {
  fill: #9370DB;
  font-size: 10px; }

#d9gqnrbh2ac .relation {
  stroke: #9370DB;
  stroke-width: 1;
  fill: none; }

#d9gqnrbh2ac #compositionStart {
  fill: #9370DB;
  stroke: #9370DB;
  stroke-width: 1; }

#d9gqnrbh2ac #compositionEnd {
  fill: #9370DB;
  stroke: #9370DB;
  stroke-width: 1; }

#d9gqnrbh2ac #aggregationStart {
  fill: #ECECFF;
  stroke: #9370DB;
  stroke-width: 1; }

#d9gqnrbh2ac #aggregationEnd {
  fill: #ECECFF;
  stroke: #9370DB;
  stroke-width: 1; }

#d9gqnrbh2ac #dependencyStart {
  fill: #9370DB;
  stroke: #9370DB;
  stroke-width: 1; }

#d9gqnrbh2ac #dependencyEnd {
  fill: #9370DB;
  stroke: #9370DB;
  stroke-width: 1; }

#d9gqnrbh2ac #extensionStart {
  fill: #9370DB;
  stroke: #9370DB;
  stroke-width: 1; }

#d9gqnrbh2ac #extensionEnd {
  fill: #9370DB;
  stroke: #9370DB;
  stroke-width: 1; }

#d9gqnrbh2ac .commit-id,
#d9gqnrbh2ac .commit-msg,
#d9gqnrbh2ac .branch-label {
  fill: lightgrey;
  color: lightgrey; }



#d9gqnrbh2ac .label{
  color:#18B14E;
}
#d9gqnrbh2ac .node rect,
#d9gqnrbh2ac .node circle,
#d9gqnrbh2ac .node ellipse,
#d9gqnrbh2ac .node polygon {
  fill: #F9FFFB;;
  stroke: #2DBD60;
  stroke-width: 1.5px;
}
#d9gqnrbh2ac .arrowheadPath{
  fill: #2DBD60;
}
#d9gqnrbh2ac .edgePath .path {
  stroke: #2DBD60;
  stroke-width: 1px;
}
#d9gqnrbh2ac .edgeLabel {
  background-color: #fff;
}
#d9gqnrbh2ac .cluster rect {
  fill: #F9FFFB !important;
  stroke: #2DBD60 !important;
  stroke-width: 1px !important;
}

#d9gqnrbh2ac .cluster text {
  fill: #F9FFFB;
}

#d9gqnrbh2ac div.mermaidTooltip {
  background: #F9FFFB;
  border: 1px solid #2DBD60;
}


#d9gqnrbh2ac .actor {
  stroke: #2DBD60;
  fill: #F9FFFB;
}

#d9gqnrbh2ac text.actor {
  fill: #2DBD60;
  stroke: none;
}

#d9gqnrbh2ac .actor-line {
  stroke: #2DBD60;
}

#d9gqnrbh2ac .messageLine0 {
  stroke-width: 1.5;
  stroke-dasharray: '2 2';
  marker-end: 'url(#arrowhead)';
  stroke: #2DBD60;
}

#d9gqnrbh2ac .messageLine1 {
  stroke-width: 1.5;
  stroke-dasharray: '2 2';
  stroke: #2DBD60;
}

#d9gqnrbh2ac #arrowhead {
  fill: #2DBD60;
}

#d9gqnrbh2ac #crosshead path {
  fill: #2DBD60 !important;
  stroke: #2DBD60 !important;
}

#d9gqnrbh2ac .messageText {
  fill: #2DBD60;
  stroke: none;
}

#d9gqnrbh2ac .labelBox {
  stroke: #2DBD60;
  fill: #F9FFFB;
}

#d9gqnrbh2ac .labelText {
  fill: #2DBD60;
  stroke: #2DBD60;
}

#d9gqnrbh2ac .loopText {
  fill: #2DBD60;
  stroke: #2DBD60;
}

#d9gqnrbh2ac .loopLine {
  stroke-width: 2;
  stroke-dasharray: '2 2';
  marker-end: 'url(#arrowhead)';
  stroke: #2DBD60;
}

#d9gqnrbh2ac .note {
  stroke: #2DBD60;
  fill: #F9FFFB;
}

#d9gqnrbh2ac .noteText {
  fill: #2DBD60;
  stroke: #2DBD60;
}


#d9gqnrbh2ac .section{
  opacity:1;
}
#d9gqnrbh2ac .section0,#d9gqnrbh2ac  .section2 {
  fill: #ECF7F0;
}

#d9gqnrbh2ac .section1,
#d9gqnrbh2ac .section3 {
  fill: #FFF;
}
#d9gqnrbh2ac .taskText0,
#d9gqnrbh2ac .taskText1,
#d9gqnrbh2ac .taskText2,
#d9gqnrbh2ac .taskText3 {
  fill: #fff;
}

#d9gqnrbh2ac .task0,
#d9gqnrbh2ac .task1,
#d9gqnrbh2ac .task2,
#d9gqnrbh2ac .task3 {
  fill: #2DBD60;
  stroke: #359F5A;
}
</style><style>#d9gqnrbh2ac {
    color: rgb(244, 244, 244);
    font: normal normal 400 normal 14px / 22.4px "Microsoft Yahei", sans-serif;
  }</style><g transform="translate(-12, -12)"><g class="output"><g class="clusters"></g><g class="edgePaths"><g class="edgePath" style="opacity: 1;"><path class="path" d="M45,20L20,45L20,70" marker-end="url(#arrowhead4469)" style="stroke: #333; stroke-width: 1.5px;fill:none"></path><defs><marker id="arrowhead4469" viewBox="0 0 10 10" refX="9" refY="5" markerUnits="strokeWidth" markerWidth="8" markerHeight="6" orient="auto"><path d="M 0 0 L 10 5 L 0 10 z" class="arrowheadPath" style="stroke-width: 1; stroke-dasharray: 1, 0;"></path></marker></defs></g><g class="edgePath" style="opacity: 1;"><path class="path" d="M45,20L70,45L70,70" marker-end="url(#arrowhead4470)" style="stroke: #333; stroke-width: 1.5px;fill:none"></path><defs><marker id="arrowhead4470" viewBox="0 0 10 10" refX="9" refY="5" markerUnits="strokeWidth" markerWidth="8" markerHeight="6" orient="auto"><path d="M 0 0 L 10 5 L 0 10 z" class="arrowheadPath" style="stroke-width: 1; stroke-dasharray: 1, 0;"></path></marker></defs></g><g class="edgePath" style="opacity: 1;"><path class="path" d="M70,70L45,95L45,120" marker-end="url(#arrowhead4471)" style="stroke: #333; stroke-width: 1.5px;fill:none"></path><defs><marker id="arrowhead4471" viewBox="0 0 10 10" refX="9" refY="5" markerUnits="strokeWidth" markerWidth="8" markerHeight="6" orient="auto"><path d="M 0 0 L 10 5 L 0 10 z" class="arrowheadPath" style="stroke-width: 1; stroke-dasharray: 1, 0;"></path></marker></defs></g><g class="edgePath" style="opacity: 1;"><path class="path" d="M70,70L95,95L95,120" marker-end="url(#arrowhead4472)" style="stroke: #333; stroke-width: 1.5px;fill:none"></path><defs><marker id="arrowhead4472" viewBox="0 0 10 10" refX="9" refY="5" markerUnits="strokeWidth" markerWidth="8" markerHeight="6" orient="auto"><path d="M 0 0 L 10 5 L 0 10 z" class="arrowheadPath" style="stroke-width: 1; stroke-dasharray: 1, 0;"></path></marker></defs></g></g><g class="edgeLabels"><g class="edgeLabel" transform="" style="opacity: 1;"><g transform="translate(0,0)" class="label"><rect rx="0" ry="0" width="0" height="0" style="fill:#e8e8e8;"></rect><text><tspan xml:space="preserve" dy="1em" x="1"></tspan></text></g></g><g class="edgeLabel" transform="" style="opacity: 1;"><g transform="translate(0,0)" class="label"><rect rx="0" ry="0" width="0" height="0" style="fill:#e8e8e8;"></rect><text><tspan xml:space="preserve" dy="1em" x="1"></tspan></text></g></g><g class="edgeLabel" transform="" style="opacity: 1;"><g transform="translate(0,0)" class="label"><rect rx="0" ry="0" width="0" height="0" style="fill:#e8e8e8;"></rect><text><tspan xml:space="preserve" dy="1em" x="1"></tspan></text></g></g><g class="edgeLabel" transform="" style="opacity: 1;"><g transform="translate(0,0)" class="label"><rect rx="0" ry="0" width="0" height="0" style="fill:#e8e8e8;"></rect><text><tspan xml:space="preserve" dy="1em" x="1"></tspan></text></g></g></g><g class="nodes"><g class="node" id="A" transform="translate(45,20)" style="opacity: 1;"><rect rx="0" ry="0" x="-10" y="-10" width="20" height="20"></rect><g class="label" transform="translate(0,0)"><g transform="translate(0,0)"><text><tspan xml:space="preserve" dy="1em" x="1">统计方法</tspan></text></g></g></g><g class="node" id="B" transform="translate(20,70)" style="opacity: 1;"><rect rx="5" ry="5" x="-10" y="-10" width="20" height="20"></rect><g class="label" transform="translate(0,0)"><g transform="translate(0,0)"><text><tspan xml:space="preserve" dy="1em" x="1">描述统计</tspan></text></g></g></g><g class="node" id="C" transform="translate(70,70)" style="opacity: 1;"><rect rx="0" ry="0" x="-10" y="-10" width="20" height="20"></rect><g class="label" transform="translate(0,0)"><g transform="translate(0,0)"><text><tspan xml:space="preserve" dy="1em" x="1">推断统计</tspan></text></g></g></g><g class="node" id="D" transform="translate(45,120)" style="opacity: 1;"><rect rx="5" ry="5" x="-10" y="-10" width="20" height="20"></rect><g class="label" transform="translate(0,0)"><g transform="translate(0,0)"><text><tspan xml:space="preserve" dy="1em" x="1">参数估计</tspan></text></g></g></g><g class="node" id="E" transform="translate(95,120)" style="opacity: 1;"><rect rx="5" ry="5" x="-10" y="-10" width="20" height="20"></rect><g class="label" transform="translate(0,0)"><g transform="translate(0,0)"><text><tspan xml:space="preserve" dy="1em" x="1">假设检验</tspan></text></g></g></g></g></g></g></svg>

估计量与估计值

1.估计量:用于估计总体参数的随机变量,如样本均值,样本比例,样本方差,例如:样本均值就是总体均值中的一个估计量
2.参数用θ表示,估计量使用θ^表示
3.估计值:估计参数时计算出来的统计量的总体值,如果样本均值为x=80,则80就是估计值

点估计与区间估计

<svg id="dxmoowmot5g" width="100%" xmlns="http://www.w3.org/2000/svg" style="max-width: 166px;" viewBox="0 0 166 116"><style>


#dxmoowmot5g .label {
  font-family: 'trebuchet ms', verdana, arial;
  color: #333; }

#dxmoowmot5g .node rect,
#dxmoowmot5g .node circle,
#dxmoowmot5g .node ellipse,
#dxmoowmot5g .node polygon {
  fill: #ECECFF;
  stroke: #9370DB;
  stroke-width: 1px; }

#dxmoowmot5g .node.clickable {
  cursor: pointer; }

#dxmoowmot5g .arrowheadPath {
  fill: #333333; }

#dxmoowmot5g .edgePath .path {
  stroke: #333333;
  stroke-width: 1.5px; }

#dxmoowmot5g .edgeLabel {
  background-color: #e8e8e8; }

#dxmoowmot5g .cluster rect {
  fill: #ffffde !important;
  stroke: #aaaa33 !important;
  stroke-width: 1px !important; }

#dxmoowmot5g .cluster text {
  fill: #333; }

#dxmoowmot5g div.mermaidTooltip {
  position: absolute;
  text-align: center;
  max-width: 200px;
  padding: 2px;
  font-family: 'trebuchet ms', verdana, arial;
  font-size: 12px;
  background: #ffffde;
  border: 1px solid #aaaa33;
  border-radius: 2px;
  pointer-events: none;
  z-index: 100; }

#dxmoowmot5g .actor {
  stroke: #CCCCFF;
  fill: #ECECFF; }

#dxmoowmot5g text.actor {
  fill: black;
  stroke: none; }

#dxmoowmot5g .actor-line {
  stroke: grey; }

#dxmoowmot5g .messageLine0 {
  stroke-width: 1.5;
  stroke-dasharray: '2 2';
  stroke: #333; }

#dxmoowmot5g .messageLine1 {
  stroke-width: 1.5;
  stroke-dasharray: '2 2';
  stroke: #333; }

#dxmoowmot5g #arrowhead {
  fill: #333; }

#dxmoowmot5g #crosshead path {
  fill: #333 !important;
  stroke: #333 !important; }

#dxmoowmot5g .messageText {
  fill: #333;
  stroke: none; }

#dxmoowmot5g .labelBox {
  stroke: #CCCCFF;
  fill: #ECECFF; }

#dxmoowmot5g .labelText {
  fill: black;
  stroke: none; }

#dxmoowmot5g .loopText {
  fill: black;
  stroke: none; }

#dxmoowmot5g .loopLine {
  stroke-width: 2;
  stroke-dasharray: '2 2';
  stroke: #CCCCFF; }

#dxmoowmot5g .note {
  stroke: #aaaa33;
  fill: #fff5ad; }

#dxmoowmot5g .noteText {
  fill: black;
  stroke: none;
  font-family: 'trebuchet ms', verdana, arial;
  font-size: 14px; }

#dxmoowmot5g .activation0 {
  fill: #f4f4f4;
  stroke: #666; }

#dxmoowmot5g .activation1 {
  fill: #f4f4f4;
  stroke: #666; }

#dxmoowmot5g .activation2 {
  fill: #f4f4f4;
  stroke: #666; }


#dxmoowmot5g .section {
  stroke: none;
  opacity: 0.2; }

#dxmoowmot5g .section0 {
  fill: rgba(102, 102, 255, 0.49); }

#dxmoowmot5g .section2 {
  fill: #fff400; }

#dxmoowmot5g .section1,
#dxmoowmot5g .section3 {
  fill: white;
  opacity: 0.2; }

#dxmoowmot5g .sectionTitle0 {
  fill: #333; }

#dxmoowmot5g .sectionTitle1 {
  fill: #333; }

#dxmoowmot5g .sectionTitle2 {
  fill: #333; }

#dxmoowmot5g .sectionTitle3 {
  fill: #333; }

#dxmoowmot5g .sectionTitle {
  text-anchor: start;
  font-size: 11px;
  text-height: 14px; }


#dxmoowmot5g .grid .tick {
  stroke: lightgrey;
  opacity: 0.3;
  shape-rendering: crispEdges; }

#dxmoowmot5g .grid path {
  stroke-width: 0; }


#dxmoowmot5g .today {
  fill: none;
  stroke: red;
  stroke-width: 2px; }



#dxmoowmot5g .task {
  stroke-width: 2; }

#dxmoowmot5g .taskText {
  text-anchor: middle;
  font-size: 11px; }

#dxmoowmot5g .taskTextOutsideRight {
  fill: black;
  text-anchor: start;
  font-size: 11px; }

#dxmoowmot5g .taskTextOutsideLeft {
  fill: black;
  text-anchor: end;
  font-size: 11px; }


#dxmoowmot5g .taskText0,
#dxmoowmot5g .taskText1,
#dxmoowmot5g .taskText2,
#dxmoowmot5g .taskText3 {
  fill: white; }

#dxmoowmot5g .task0,
#dxmoowmot5g .task1,
#dxmoowmot5g .task2,
#dxmoowmot5g .task3 {
  fill: #8a90dd;
  stroke: #534fbc; }

#dxmoowmot5g .taskTextOutside0,
#dxmoowmot5g .taskTextOutside2 {
  fill: black; }

#dxmoowmot5g .taskTextOutside1,
#dxmoowmot5g .taskTextOutside3 {
  fill: black; }


#dxmoowmot5g .active0,
#dxmoowmot5g .active1,
#dxmoowmot5g .active2,
#dxmoowmot5g .active3 {
  fill: #bfc7ff;
  stroke: #534fbc; }

#dxmoowmot5g .activeText0,
#dxmoowmot5g .activeText1,
#dxmoowmot5g .activeText2,
#dxmoowmot5g .activeText3 {
  fill: black !important; }


#dxmoowmot5g .done0,
#dxmoowmot5g .done1,
#dxmoowmot5g .done2,
#dxmoowmot5g .done3 {
  stroke: grey;
  fill: lightgrey;
  stroke-width: 2; }

#dxmoowmot5g .doneText0,
#dxmoowmot5g .doneText1,
#dxmoowmot5g .doneText2,
#dxmoowmot5g .doneText3 {
  fill: black !important; }


#dxmoowmot5g .crit0,
#dxmoowmot5g .crit1,
#dxmoowmot5g .crit2,
#dxmoowmot5g .crit3 {
  stroke: #ff8888;
  fill: red;
  stroke-width: 2; }

#dxmoowmot5g .activeCrit0,
#dxmoowmot5g .activeCrit1,
#dxmoowmot5g .activeCrit2,
#dxmoowmot5g .activeCrit3 {
  stroke: #ff8888;
  fill: #bfc7ff;
  stroke-width: 2; }

#dxmoowmot5g .doneCrit0,
#dxmoowmot5g .doneCrit1,
#dxmoowmot5g .doneCrit2,
#dxmoowmot5g .doneCrit3 {
  stroke: #ff8888;
  fill: lightgrey;
  stroke-width: 2;
  cursor: pointer;
  shape-rendering: crispEdges; }

#dxmoowmot5g .doneCritText0,
#dxmoowmot5g .doneCritText1,
#dxmoowmot5g .doneCritText2,
#dxmoowmot5g .doneCritText3 {
  fill: black !important; }

#dxmoowmot5g .activeCritText0,
#dxmoowmot5g .activeCritText1,
#dxmoowmot5g .activeCritText2,
#dxmoowmot5g .activeCritText3 {
  fill: black !important; }

#dxmoowmot5g .titleText {
  text-anchor: middle;
  font-size: 18px;
  fill: black; }

#dxmoowmot5g g.classGroup text {
  fill: #9370DB;
  stroke: none;
  font-family: 'trebuchet ms', verdana, arial;
  font-size: 10px; }

#dxmoowmot5g g.classGroup rect {
  fill: #ECECFF;
  stroke: #9370DB; }

#dxmoowmot5g g.classGroup line {
  stroke: #9370DB;
  stroke-width: 1; }

#dxmoowmot5g .classLabel .box {
  stroke: none;
  stroke-width: 0;
  fill: #ECECFF;
  opacity: 0.5; }

#dxmoowmot5g .classLabel .label {
  fill: #9370DB;
  font-size: 10px; }

#dxmoowmot5g .relation {
  stroke: #9370DB;
  stroke-width: 1;
  fill: none; }

#dxmoowmot5g #compositionStart {
  fill: #9370DB;
  stroke: #9370DB;
  stroke-width: 1; }

#dxmoowmot5g #compositionEnd {
  fill: #9370DB;
  stroke: #9370DB;
  stroke-width: 1; }

#dxmoowmot5g #aggregationStart {
  fill: #ECECFF;
  stroke: #9370DB;
  stroke-width: 1; }

#dxmoowmot5g #aggregationEnd {
  fill: #ECECFF;
  stroke: #9370DB;
  stroke-width: 1; }

#dxmoowmot5g #dependencyStart {
  fill: #9370DB;
  stroke: #9370DB;
  stroke-width: 1; }

#dxmoowmot5g #dependencyEnd {
  fill: #9370DB;
  stroke: #9370DB;
  stroke-width: 1; }

#dxmoowmot5g #extensionStart {
  fill: #9370DB;
  stroke: #9370DB;
  stroke-width: 1; }

#dxmoowmot5g #extensionEnd {
  fill: #9370DB;
  stroke: #9370DB;
  stroke-width: 1; }

#dxmoowmot5g .commit-id,
#dxmoowmot5g .commit-msg,
#dxmoowmot5g .branch-label {
  fill: lightgrey;
  color: lightgrey; }



#dxmoowmot5g .label{
  color:#18B14E;
}
#dxmoowmot5g .node rect,
#dxmoowmot5g .node circle,
#dxmoowmot5g .node ellipse,
#dxmoowmot5g .node polygon {
  fill: #F9FFFB;;
  stroke: #2DBD60;
  stroke-width: 1.5px;
}
#dxmoowmot5g .arrowheadPath{
  fill: #2DBD60;
}
#dxmoowmot5g .edgePath .path {
  stroke: #2DBD60;
  stroke-width: 1px;
}
#dxmoowmot5g .edgeLabel {
  background-color: #fff;
}
#dxmoowmot5g .cluster rect {
  fill: #F9FFFB !important;
  stroke: #2DBD60 !important;
  stroke-width: 1px !important;
}

#dxmoowmot5g .cluster text {
  fill: #F9FFFB;
}

#dxmoowmot5g div.mermaidTooltip {
  background: #F9FFFB;
  border: 1px solid #2DBD60;
}


#dxmoowmot5g .actor {
  stroke: #2DBD60;
  fill: #F9FFFB;
}

#dxmoowmot5g text.actor {
  fill: #2DBD60;
  stroke: none;
}

#dxmoowmot5g .actor-line {
  stroke: #2DBD60;
}

#dxmoowmot5g .messageLine0 {
  stroke-width: 1.5;
  stroke-dasharray: '2 2';
  marker-end: 'url(#arrowhead)';
  stroke: #2DBD60;
}

#dxmoowmot5g .messageLine1 {
  stroke-width: 1.5;
  stroke-dasharray: '2 2';
  stroke: #2DBD60;
}

#dxmoowmot5g #arrowhead {
  fill: #2DBD60;
}

#dxmoowmot5g #crosshead path {
  fill: #2DBD60 !important;
  stroke: #2DBD60 !important;
}

#dxmoowmot5g .messageText {
  fill: #2DBD60;
  stroke: none;
}

#dxmoowmot5g .labelBox {
  stroke: #2DBD60;
  fill: #F9FFFB;
}

#dxmoowmot5g .labelText {
  fill: #2DBD60;
  stroke: #2DBD60;
}

#dxmoowmot5g .loopText {
  fill: #2DBD60;
  stroke: #2DBD60;
}

#dxmoowmot5g .loopLine {
  stroke-width: 2;
  stroke-dasharray: '2 2';
  marker-end: 'url(#arrowhead)';
  stroke: #2DBD60;
}

#dxmoowmot5g .note {
  stroke: #2DBD60;
  fill: #F9FFFB;
}

#dxmoowmot5g .noteText {
  fill: #2DBD60;
  stroke: #2DBD60;
}


#dxmoowmot5g .section{
  opacity:1;
}
#dxmoowmot5g .section0,#dxmoowmot5g  .section2 {
  fill: #ECF7F0;
}

#dxmoowmot5g .section1,
#dxmoowmot5g .section3 {
  fill: #FFF;
}
#dxmoowmot5g .taskText0,
#dxmoowmot5g .taskText1,
#dxmoowmot5g .taskText2,
#dxmoowmot5g .taskText3 {
  fill: #fff;
}

#dxmoowmot5g .task0,
#dxmoowmot5g .task1,
#dxmoowmot5g .task2,
#dxmoowmot5g .task3 {
  fill: #2DBD60;
  stroke: #359F5A;
}
</style><style>#dxmoowmot5g {
    color: rgb(244, 244, 244);
    font: normal normal 400 normal 14px / 22.4px "Microsoft Yahei", sans-serif;
  }</style><g transform="translate(-12, -12)"><g class="output"><g class="clusters"></g><g class="edgePaths"><g class="edgePath" style="opacity: 1;"><path class="path" d="M120,20L95,45L95,70" marker-end="url(#arrowhead4488)" style="stroke: #333; stroke-width: 1.5px;fill:none"></path><defs><marker id="arrowhead4488" viewBox="0 0 10 10" refX="9" refY="5" markerUnits="strokeWidth" markerWidth="8" markerHeight="6" orient="auto"><path d="M 0 0 L 10 5 L 0 10 z" class="arrowheadPath" style="stroke-width: 1; stroke-dasharray: 1, 0;"></path></marker></defs></g><g class="edgePath" style="opacity: 1;"><path class="path" d="M120,20L145,45L145,70" marker-end="url(#arrowhead4489)" style="stroke: #333; stroke-width: 1.5px;fill:none"></path><defs><marker id="arrowhead4489" viewBox="0 0 10 10" refX="9" refY="5" markerUnits="strokeWidth" markerWidth="8" markerHeight="6" orient="auto"><path d="M 0 0 L 10 5 L 0 10 z" class="arrowheadPath" style="stroke-width: 1; stroke-dasharray: 1, 0;"></path></marker></defs></g><g class="edgePath" style="opacity: 1;"><path class="path" d="M95,70L20,95L20,120" marker-end="url(#arrowhead4490)" style="stroke: #333; stroke-width: 1.5px;fill:none"></path><defs><marker id="arrowhead4490" viewBox="0 0 10 10" refX="9" refY="5" markerUnits="strokeWidth" markerWidth="8" markerHeight="6" orient="auto"><path d="M 0 0 L 10 5 L 0 10 z" class="arrowheadPath" style="stroke-width: 1; stroke-dasharray: 1, 0;"></path></marker></defs></g><g class="edgePath" style="opacity: 1;"><path class="path" d="M95,70L70,95L70,120" marker-end="url(#arrowhead4491)" style="stroke: #333; stroke-width: 1.5px;fill:none"></path><defs><marker id="arrowhead4491" viewBox="0 0 10 10" refX="9" refY="5" markerUnits="strokeWidth" markerWidth="8" markerHeight="6" orient="auto"><path d="M 0 0 L 10 5 L 0 10 z" class="arrowheadPath" style="stroke-width: 1; stroke-dasharray: 1, 0;"></path></marker></defs></g><g class="edgePath" style="opacity: 1;"><path class="path" d="M95,70L120,95L120,120" marker-end="url(#arrowhead4492)" style="stroke: #333; stroke-width: 1.5px;fill:none"></path><defs><marker id="arrowhead4492" viewBox="0 0 10 10" refX="9" refY="5" markerUnits="strokeWidth" markerWidth="8" markerHeight="6" orient="auto"><path d="M 0 0 L 10 5 L 0 10 z" class="arrowheadPath" style="stroke-width: 1; stroke-dasharray: 1, 0;"></path></marker></defs></g><g class="edgePath" style="opacity: 1;"><path class="path" d="M95,70L170,95L170,120" marker-end="url(#arrowhead4493)" style="stroke: #333; stroke-width: 1.5px;fill:none"></path><defs><marker id="arrowhead4493" viewBox="0 0 10 10" refX="9" refY="5" markerUnits="strokeWidth" markerWidth="8" markerHeight="6" orient="auto"><path d="M 0 0 L 10 5 L 0 10 z" class="arrowheadPath" style="stroke-width: 1; stroke-dasharray: 1, 0;"></path></marker></defs></g></g><g class="edgeLabels"><g class="edgeLabel" transform="" style="opacity: 1;"><g transform="translate(0,0)" class="label"><rect rx="0" ry="0" width="0" height="0" style="fill:#e8e8e8;"></rect><text><tspan xml:space="preserve" dy="1em" x="1"></tspan></text></g></g><g class="edgeLabel" transform="" style="opacity: 1;"><g transform="translate(0,0)" class="label"><rect rx="0" ry="0" width="0" height="0" style="fill:#e8e8e8;"></rect><text><tspan xml:space="preserve" dy="1em" x="1"></tspan></text></g></g><g class="edgeLabel" transform="" style="opacity: 1;"><g transform="translate(0,0)" class="label"><rect rx="0" ry="0" width="0" height="0" style="fill:#e8e8e8;"></rect><text><tspan xml:space="preserve" dy="1em" x="1"></tspan></text></g></g><g class="edgeLabel" transform="" style="opacity: 1;"><g transform="translate(0,0)" class="label"><rect rx="0" ry="0" width="0" height="0" style="fill:#e8e8e8;"></rect><text><tspan xml:space="preserve" dy="1em" x="1"></tspan></text></g></g><g class="edgeLabel" transform="" style="opacity: 1;"><g transform="translate(0,0)" class="label"><rect rx="0" ry="0" width="0" height="0" style="fill:#e8e8e8;"></rect><text><tspan xml:space="preserve" dy="1em" x="1"></tspan></text></g></g><g class="edgeLabel" transform="" style="opacity: 1;"><g transform="translate(0,0)" class="label"><rect rx="0" ry="0" width="0" height="0" style="fill:#e8e8e8;"></rect><text><tspan xml:space="preserve" dy="1em" x="1"></tspan></text></g></g></g><g class="nodes"><g class="node" id="A" transform="translate(120,20)" style="opacity: 1;"><rect rx="0" ry="0" x="-10" y="-10" width="20" height="20"></rect><g class="label" transform="translate(0,0)"><g transform="translate(0,0)"><text><tspan xml:space="preserve" dy="1em" x="1">估计方法</tspan></text></g></g></g><g class="node" id="B" transform="translate(95,70)" style="opacity: 1;"><rect rx="0" ry="0" x="-10" y="-10" width="20" height="20"></rect><g class="label" transform="translate(0,0)"><g transform="translate(0,0)"><text><tspan xml:space="preserve" dy="1em" x="1">点估计</tspan></text></g></g></g><g class="node" id="C" transform="translate(145,70)" style="opacity: 1;"><rect rx="5" ry="5" x="-10" y="-10" width="20" height="20"></rect><g class="label" transform="translate(0,0)"><g transform="translate(0,0)"><text><tspan xml:space="preserve" dy="1em" x="1">区间估计</tspan></text></g></g></g><g class="node" id="D" transform="translate(20,120)" style="opacity: 1;"><rect rx="5" ry="5" x="-10" y="-10" width="20" height="20"></rect><g class="label" transform="translate(0,0)"><g transform="translate(0,0)"><text><tspan xml:space="preserve" dy="1em" x="1">矩估计法</tspan></text></g></g></g><g class="node" id="E" transform="translate(70,120)" style="opacity: 1;"><rect rx="5" ry="5" x="-10" y="-10" width="20" height="20"></rect><g class="label" transform="translate(0,0)"><g transform="translate(0,0)"><text><tspan xml:space="preserve" dy="1em" x="1">顺序统计量法</tspan></text></g></g></g><g class="node" id="F" transform="translate(120,120)" style="opacity: 1;"><rect rx="5" ry="5" x="-10" y="-10" width="20" height="20"></rect><g class="label" transform="translate(0,0)"><g transform="translate(0,0)"><text><tspan xml:space="preserve" dy="1em" x="1">最大似然法</tspan></text></g></g></g><g class="node" id="G" transform="translate(170,120)" style="opacity: 1;"><rect rx="5" ry="5" x="-10" y="-10" width="20" height="20"></rect><g class="label" transform="translate(0,0)"><g transform="translate(0,0)"><text><tspan xml:space="preserve" dy="1em" x="1">最小二乘法</tspan></text></g></g></g></g></g></g></svg>

点估计:用样本的估计量直接作为总体参数的估计值,用样本均值直接作为总体均值的估计
用两个样本均值之差直接作为总体均值之差的估计
没有给出估计值接近总体参数程度的信息

区间估计:在点估计的总体基础上,给出总体参数估计的一个区间范围,该区间由样本统计量加减抽样误差而得到的。
根据样本统计量的抽样分布能够对样本统计量与总体参数的接近程度给出一个概率统计量,比如某班级平均分数在75-85分之间, 置信水平是95%
置信水平:将构造置信区间的步骤重复很多次,置信区间包含总体参数真值的次数所占的比例称为置信水平
常用的置信水平有99%,95%,90%
由样本统计量所构造的总体参数的估计区间称为置信区间
统计学家在某种程度上确信这个区间会包含真正的总体参数,所以给它取名为置信区间
用一个具体的样本所构造的区间是一个特定的区间,无法知道这个样本所产生的区间是否包含总体参数的真值。只能是希望这个区间是大量包含总体参数真值的区间中的一个,但是它也可能是少数几个不包含参数真值的区间中的一个。

评价估计量的标准---无偏性

无偏性估计量抽样分布的数学期望等于被估计的总体参数
有效性对同一总体参数的两个无偏点估计量,有更小标准差的估计量更有效
一致性随着样本容量的增大,估计量的值越来越接近被估计的总体参数

一个总体参数的区间估计

总体参数符号表示样本统计量
均值 μ x
比例 π P
方差 σ2 s2

总体均值的区间估计

正态总体、σ2已知,或非正态总体、大样本
假定条件:总体服从正态分布,且方差(σ2)已知
如果不是正态分布,可由正态分布来近似(大样本n>=30)
使用正态分布统计量z
总体均值μ1α的置信水平下的公式为
x±z2α
x±zns(α未知)


正态总体、σ2未知、小样本
1.假定条件

  • 总体服从正态分布,且方差(σ2)未知
  • 小样本(n<30)
    2.使用t分布统计量
    t=nsxμ t(n1)
    3.总体均值μ1α置信水平下的置信区间
    x±t2αns
    t分布t分布式类似正态分布的一种对称分布,它通常要比正态分布平坦和分散,一个特定的分布依赖于称之为自由度的参数,随着自由度的增大,分布更趋向于正态分布。

总体比例的区间估计

1.假定条件

  • 总体服从二项分布
  • 可以由正态分布来近似
    2.使用正态分布统计量 Z
    z=nπ(1π)pπ N(0,1)
    3.总体比例π1α置信水平下的置信区间
    p±z2αnπ(1π)p±z2αnp(1p),π未知时

总体方差的区间估计

1.估计一个总体的方差或标准差
2.假设总体服从正态分布
3.总体方差的点估计量为s2,且σ2(n1)s2 χ2(n1)
4.总体方差在1α置信水平下的置信区间为χ2α2(n1)(n1)s2<=σ2<=χ122α(n1)(n1)s2

<svg id="d585v4c9ynf" width="100%" xmlns="http://www.w3.org/2000/svg" style="max-width: 216px;" viewBox="0 0 216 216"><style>


#d585v4c9ynf .label {
  font-family: 'trebuchet ms', verdana, arial;
  color: #333; }

#d585v4c9ynf .node rect,
#d585v4c9ynf .node circle,
#d585v4c9ynf .node ellipse,
#d585v4c9ynf .node polygon {
  fill: #ECECFF;
  stroke: #9370DB;
  stroke-width: 1px; }

#d585v4c9ynf .node.clickable {
  cursor: pointer; }

#d585v4c9ynf .arrowheadPath {
  fill: #333333; }

#d585v4c9ynf .edgePath .path {
  stroke: #333333;
  stroke-width: 1.5px; }

#d585v4c9ynf .edgeLabel {
  background-color: #e8e8e8; }

#d585v4c9ynf .cluster rect {
  fill: #ffffde !important;
  stroke: #aaaa33 !important;
  stroke-width: 1px !important; }

#d585v4c9ynf .cluster text {
  fill: #333; }

#d585v4c9ynf div.mermaidTooltip {
  position: absolute;
  text-align: center;
  max-width: 200px;
  padding: 2px;
  font-family: 'trebuchet ms', verdana, arial;
  font-size: 12px;
  background: #ffffde;
  border: 1px solid #aaaa33;
  border-radius: 2px;
  pointer-events: none;
  z-index: 100; }

#d585v4c9ynf .actor {
  stroke: #CCCCFF;
  fill: #ECECFF; }

#d585v4c9ynf text.actor {
  fill: black;
  stroke: none; }

#d585v4c9ynf .actor-line {
  stroke: grey; }

#d585v4c9ynf .messageLine0 {
  stroke-width: 1.5;
  stroke-dasharray: '2 2';
  stroke: #333; }

#d585v4c9ynf .messageLine1 {
  stroke-width: 1.5;
  stroke-dasharray: '2 2';
  stroke: #333; }

#d585v4c9ynf #arrowhead {
  fill: #333; }

#d585v4c9ynf #crosshead path {
  fill: #333 !important;
  stroke: #333 !important; }

#d585v4c9ynf .messageText {
  fill: #333;
  stroke: none; }

#d585v4c9ynf .labelBox {
  stroke: #CCCCFF;
  fill: #ECECFF; }

#d585v4c9ynf .labelText {
  fill: black;
  stroke: none; }

#d585v4c9ynf .loopText {
  fill: black;
  stroke: none; }

#d585v4c9ynf .loopLine {
  stroke-width: 2;
  stroke-dasharray: '2 2';
  stroke: #CCCCFF; }

#d585v4c9ynf .note {
  stroke: #aaaa33;
  fill: #fff5ad; }

#d585v4c9ynf .noteText {
  fill: black;
  stroke: none;
  font-family: 'trebuchet ms', verdana, arial;
  font-size: 14px; }

#d585v4c9ynf .activation0 {
  fill: #f4f4f4;
  stroke: #666; }

#d585v4c9ynf .activation1 {
  fill: #f4f4f4;
  stroke: #666; }

#d585v4c9ynf .activation2 {
  fill: #f4f4f4;
  stroke: #666; }


#d585v4c9ynf .section {
  stroke: none;
  opacity: 0.2; }

#d585v4c9ynf .section0 {
  fill: rgba(102, 102, 255, 0.49); }

#d585v4c9ynf .section2 {
  fill: #fff400; }

#d585v4c9ynf .section1,
#d585v4c9ynf .section3 {
  fill: white;
  opacity: 0.2; }

#d585v4c9ynf .sectionTitle0 {
  fill: #333; }

#d585v4c9ynf .sectionTitle1 {
  fill: #333; }

#d585v4c9ynf .sectionTitle2 {
  fill: #333; }

#d585v4c9ynf .sectionTitle3 {
  fill: #333; }

#d585v4c9ynf .sectionTitle {
  text-anchor: start;
  font-size: 11px;
  text-height: 14px; }


#d585v4c9ynf .grid .tick {
  stroke: lightgrey;
  opacity: 0.3;
  shape-rendering: crispEdges; }

#d585v4c9ynf .grid path {
  stroke-width: 0; }


#d585v4c9ynf .today {
  fill: none;
  stroke: red;
  stroke-width: 2px; }



#d585v4c9ynf .task {
  stroke-width: 2; }

#d585v4c9ynf .taskText {
  text-anchor: middle;
  font-size: 11px; }

#d585v4c9ynf .taskTextOutsideRight {
  fill: black;
  text-anchor: start;
  font-size: 11px; }

#d585v4c9ynf .taskTextOutsideLeft {
  fill: black;
  text-anchor: end;
  font-size: 11px; }


#d585v4c9ynf .taskText0,
#d585v4c9ynf .taskText1,
#d585v4c9ynf .taskText2,
#d585v4c9ynf .taskText3 {
  fill: white; }

#d585v4c9ynf .task0,
#d585v4c9ynf .task1,
#d585v4c9ynf .task2,
#d585v4c9ynf .task3 {
  fill: #8a90dd;
  stroke: #534fbc; }

#d585v4c9ynf .taskTextOutside0,
#d585v4c9ynf .taskTextOutside2 {
  fill: black; }

#d585v4c9ynf .taskTextOutside1,
#d585v4c9ynf .taskTextOutside3 {
  fill: black; }


#d585v4c9ynf .active0,
#d585v4c9ynf .active1,
#d585v4c9ynf .active2,
#d585v4c9ynf .active3 {
  fill: #bfc7ff;
  stroke: #534fbc; }

#d585v4c9ynf .activeText0,
#d585v4c9ynf .activeText1,
#d585v4c9ynf .activeText2,
#d585v4c9ynf .activeText3 {
  fill: black !important; }


#d585v4c9ynf .done0,
#d585v4c9ynf .done1,
#d585v4c9ynf .done2,
#d585v4c9ynf .done3 {
  stroke: grey;
  fill: lightgrey;
  stroke-width: 2; }

#d585v4c9ynf .doneText0,
#d585v4c9ynf .doneText1,
#d585v4c9ynf .doneText2,
#d585v4c9ynf .doneText3 {
  fill: black !important; }


#d585v4c9ynf .crit0,
#d585v4c9ynf .crit1,
#d585v4c9ynf .crit2,
#d585v4c9ynf .crit3 {
  stroke: #ff8888;
  fill: red;
  stroke-width: 2; }

#d585v4c9ynf .activeCrit0,
#d585v4c9ynf .activeCrit1,
#d585v4c9ynf .activeCrit2,
#d585v4c9ynf .activeCrit3 {
  stroke: #ff8888;
  fill: #bfc7ff;
  stroke-width: 2; }

#d585v4c9ynf .doneCrit0,
#d585v4c9ynf .doneCrit1,
#d585v4c9ynf .doneCrit2,
#d585v4c9ynf .doneCrit3 {
  stroke: #ff8888;
  fill: lightgrey;
  stroke-width: 2;
  cursor: pointer;
  shape-rendering: crispEdges; }

#d585v4c9ynf .doneCritText0,
#d585v4c9ynf .doneCritText1,
#d585v4c9ynf .doneCritText2,
#d585v4c9ynf .doneCritText3 {
  fill: black !important; }

#d585v4c9ynf .activeCritText0,
#d585v4c9ynf .activeCritText1,
#d585v4c9ynf .activeCritText2,
#d585v4c9ynf .activeCritText3 {
  fill: black !important; }

#d585v4c9ynf .titleText {
  text-anchor: middle;
  font-size: 18px;
  fill: black; }

#d585v4c9ynf g.classGroup text {
  fill: #9370DB;
  stroke: none;
  font-family: 'trebuchet ms', verdana, arial;
  font-size: 10px; }

#d585v4c9ynf g.classGroup rect {
  fill: #ECECFF;
  stroke: #9370DB; }

#d585v4c9ynf g.classGroup line {
  stroke: #9370DB;
  stroke-width: 1; }

#d585v4c9ynf .classLabel .box {
  stroke: none;
  stroke-width: 0;
  fill: #ECECFF;
  opacity: 0.5; }

#d585v4c9ynf .classLabel .label {
  fill: #9370DB;
  font-size: 10px; }

#d585v4c9ynf .relation {
  stroke: #9370DB;
  stroke-width: 1;
  fill: none; }

#d585v4c9ynf #compositionStart {
  fill: #9370DB;
  stroke: #9370DB;
  stroke-width: 1; }

#d585v4c9ynf #compositionEnd {
  fill: #9370DB;
  stroke: #9370DB;
  stroke-width: 1; }

#d585v4c9ynf #aggregationStart {
  fill: #ECECFF;
  stroke: #9370DB;
  stroke-width: 1; }

#d585v4c9ynf #aggregationEnd {
  fill: #ECECFF;
  stroke: #9370DB;
  stroke-width: 1; }

#d585v4c9ynf #dependencyStart {
  fill: #9370DB;
  stroke: #9370DB;
  stroke-width: 1; }

#d585v4c9ynf #dependencyEnd {
  fill: #9370DB;
  stroke: #9370DB;
  stroke-width: 1; }

#d585v4c9ynf #extensionStart {
  fill: #9370DB;
  stroke: #9370DB;
  stroke-width: 1; }

#d585v4c9ynf #extensionEnd {
  fill: #9370DB;
  stroke: #9370DB;
  stroke-width: 1; }

#d585v4c9ynf .commit-id,
#d585v4c9ynf .commit-msg,
#d585v4c9ynf .branch-label {
  fill: lightgrey;
  color: lightgrey; }



#d585v4c9ynf .label{
  color:#18B14E;
}
#d585v4c9ynf .node rect,
#d585v4c9ynf .node circle,
#d585v4c9ynf .node ellipse,
#d585v4c9ynf .node polygon {
  fill: #F9FFFB;;
  stroke: #2DBD60;
  stroke-width: 1.5px;
}
#d585v4c9ynf .arrowheadPath{
  fill: #2DBD60;
}
#d585v4c9ynf .edgePath .path {
  stroke: #2DBD60;
  stroke-width: 1px;
}
#d585v4c9ynf .edgeLabel {
  background-color: #fff;
}
#d585v4c9ynf .cluster rect {
  fill: #F9FFFB !important;
  stroke: #2DBD60 !important;
  stroke-width: 1px !important;
}

#d585v4c9ynf .cluster text {
  fill: #F9FFFB;
}

#d585v4c9ynf div.mermaidTooltip {
  background: #F9FFFB;
  border: 1px solid #2DBD60;
}


#d585v4c9ynf .actor {
  stroke: #2DBD60;
  fill: #F9FFFB;
}

#d585v4c9ynf text.actor {
  fill: #2DBD60;
  stroke: none;
}

#d585v4c9ynf .actor-line {
  stroke: #2DBD60;
}

#d585v4c9ynf .messageLine0 {
  stroke-width: 1.5;
  stroke-dasharray: '2 2';
  marker-end: 'url(#arrowhead)';
  stroke: #2DBD60;
}

#d585v4c9ynf .messageLine1 {
  stroke-width: 1.5;
  stroke-dasharray: '2 2';
  stroke: #2DBD60;
}

#d585v4c9ynf #arrowhead {
  fill: #2DBD60;
}

#d585v4c9ynf #crosshead path {
  fill: #2DBD60 !important;
  stroke: #2DBD60 !important;
}

#d585v4c9ynf .messageText {
  fill: #2DBD60;
  stroke: none;
}

#d585v4c9ynf .labelBox {
  stroke: #2DBD60;
  fill: #F9FFFB;
}

#d585v4c9ynf .labelText {
  fill: #2DBD60;
  stroke: #2DBD60;
}

#d585v4c9ynf .loopText {
  fill: #2DBD60;
  stroke: #2DBD60;
}

#d585v4c9ynf .loopLine {
  stroke-width: 2;
  stroke-dasharray: '2 2';
  marker-end: 'url(#arrowhead)';
  stroke: #2DBD60;
}

#d585v4c9ynf .note {
  stroke: #2DBD60;
  fill: #F9FFFB;
}

#d585v4c9ynf .noteText {
  fill: #2DBD60;
  stroke: #2DBD60;
}


#d585v4c9ynf .section{
  opacity:1;
}
#d585v4c9ynf .section0,#d585v4c9ynf  .section2 {
  fill: #ECF7F0;
}

#d585v4c9ynf .section1,
#d585v4c9ynf .section3 {
  fill: #FFF;
}
#d585v4c9ynf .taskText0,
#d585v4c9ynf .taskText1,
#d585v4c9ynf .taskText2,
#d585v4c9ynf .taskText3 {
  fill: #fff;
}

#d585v4c9ynf .task0,
#d585v4c9ynf .task1,
#d585v4c9ynf .task2,
#d585v4c9ynf .task3 {
  fill: #2DBD60;
  stroke: #359F5A;
}
</style><style>#d585v4c9ynf {
    color: rgb(244, 244, 244);
    font: normal normal 400 normal 14px / 22.4px "Microsoft Yahei", sans-serif;
  }</style><g transform="translate(-12, -12)"><g class="output"><g class="clusters"></g><g class="edgePaths"><g class="edgePath" style="opacity: 1;"><path class="path" d="M170,20L70,45L70,70" marker-end="url(#arrowhead4524)" style="stroke: #333; stroke-width: 1.5px;fill:none"></path><defs><marker id="arrowhead4524" viewBox="0 0 10 10" refX="9" refY="5" markerUnits="strokeWidth" markerWidth="8" markerHeight="6" orient="auto"><path d="M 0 0 L 10 5 L 0 10 z" class="arrowheadPath" style="stroke-width: 1; stroke-dasharray: 1, 0;"></path></marker></defs></g><g class="edgePath" style="opacity: 1;"><path class="path" d="M170,20L170,45L170,70" marker-end="url(#arrowhead4525)" style="stroke: #333; stroke-width: 1.5px;fill:none"></path><defs><marker id="arrowhead4525" viewBox="0 0 10 10" refX="9" refY="5" markerUnits="strokeWidth" markerWidth="8" markerHeight="6" orient="auto"><path d="M 0 0 L 10 5 L 0 10 z" class="arrowheadPath" style="stroke-width: 1; stroke-dasharray: 1, 0;"></path></marker></defs></g><g class="edgePath" style="opacity: 1;"><path class="path" d="M170,20L220,45L220,70" marker-end="url(#arrowhead4526)" style="stroke: #333; stroke-width: 1.5px;fill:none"></path><defs><marker id="arrowhead4526" viewBox="0 0 10 10" refX="9" refY="5" markerUnits="strokeWidth" markerWidth="8" markerHeight="6" orient="auto"><path d="M 0 0 L 10 5 L 0 10 z" class="arrowheadPath" style="stroke-width: 1; stroke-dasharray: 1, 0;"></path></marker></defs></g><g class="edgePath" style="opacity: 1;"><path class="path" d="M70,70L120,95L120,120" marker-end="url(#arrowhead4527)" style="stroke: #333; stroke-width: 1.5px;fill:none"></path><defs><marker id="arrowhead4527" viewBox="0 0 10 10" refX="9" refY="5" markerUnits="strokeWidth" markerWidth="8" markerHeight="6" orient="auto"><path d="M 0 0 L 10 5 L 0 10 z" class="arrowheadPath" style="stroke-width: 1; stroke-dasharray: 1, 0;"></path></marker></defs></g><g class="edgePath" style="opacity: 1;"><path class="path" d="M70,70L45,95L45,120" marker-end="url(#arrowhead4528)" style="stroke: #333; stroke-width: 1.5px;fill:none"></path><defs><marker id="arrowhead4528" viewBox="0 0 10 10" refX="9" refY="5" markerUnits="strokeWidth" markerWidth="8" markerHeight="6" orient="auto"><path d="M 0 0 L 10 5 L 0 10 z" class="arrowheadPath" style="stroke-width: 1; stroke-dasharray: 1, 0;"></path></marker></defs></g><g class="edgePath" style="opacity: 1;"><path class="path" d="M45,120L20,145L20,170" marker-end="url(#arrowhead4529)" style="stroke: #333; stroke-width: 1.5px;fill:none"></path><defs><marker id="arrowhead4529" viewBox="0 0 10 10" refX="9" refY="5" markerUnits="strokeWidth" markerWidth="8" markerHeight="6" orient="auto"><path d="M 0 0 L 10 5 L 0 10 z" class="arrowheadPath" style="stroke-width: 1; stroke-dasharray: 1, 0;"></path></marker></defs></g><g class="edgePath" style="opacity: 1;"><path class="path" d="M45,120L70,145L70,170" marker-end="url(#arrowhead4530)" style="stroke: #333; stroke-width: 1.5px;fill:none"></path><defs><marker id="arrowhead4530" viewBox="0 0 10 10" refX="9" refY="5" markerUnits="strokeWidth" markerWidth="8" markerHeight="6" orient="auto"><path d="M 0 0 L 10 5 L 0 10 z" class="arrowheadPath" style="stroke-width: 1; stroke-dasharray: 1, 0;"></path></marker></defs></g><g class="edgePath" style="opacity: 1;"><path class="path" d="M120,120L120,145L120,170" marker-end="url(#arrowhead4531)" style="stroke: #333; stroke-width: 1.5px;fill:none"></path><defs><marker id="arrowhead4531" viewBox="0 0 10 10" refX="9" refY="5" markerUnits="strokeWidth" markerWidth="8" markerHeight="6" orient="auto"><path d="M 0 0 L 10 5 L 0 10 z" class="arrowheadPath" style="stroke-width: 1; stroke-dasharray: 1, 0;"></path></marker></defs></g><g class="edgePath" style="opacity: 1;"><path class="path" d="M20,170L20,195L20,220" marker-end="url(#arrowhead4532)" style="stroke: #333; stroke-width: 1.5px;fill:none"></path><defs><marker id="arrowhead4532" viewBox="0 0 10 10" refX="9" refY="5" markerUnits="strokeWidth" markerWidth="8" markerHeight="6" orient="auto"><path d="M 0 0 L 10 5 L 0 10 z" class="arrowheadPath" style="stroke-width: 1; stroke-dasharray: 1, 0;"></path></marker></defs></g><g class="edgePath" style="opacity: 1;"><path class="path" d="M70,170L70,195L70,220" marker-end="url(#arrowhead4533)" style="stroke: #333; stroke-width: 1.5px;fill:none"></path><defs><marker id="arrowhead4533" viewBox="0 0 10 10" refX="9" refY="5" markerUnits="strokeWidth" markerWidth="8" markerHeight="6" orient="auto"><path d="M 0 0 L 10 5 L 0 10 z" class="arrowheadPath" style="stroke-width: 1; stroke-dasharray: 1, 0;"></path></marker></defs></g><g class="edgePath" style="opacity: 1;"><path class="path" d="M170,70L170,95L170,120" marker-end="url(#arrowhead4534)" style="stroke: #333; stroke-width: 1.5px;fill:none"></path><defs><marker id="arrowhead4534" viewBox="0 0 10 10" refX="9" refY="5" markerUnits="strokeWidth" markerWidth="8" markerHeight="6" orient="auto"><path d="M 0 0 L 10 5 L 0 10 z" class="arrowheadPath" style="stroke-width: 1; stroke-dasharray: 1, 0;"></path></marker></defs></g><g class="edgePath" style="opacity: 1;"><path class="path" d="M170,120L170,145L170,170" marker-end="url(#arrowhead4535)" style="stroke: #333; stroke-width: 1.5px;fill:none"></path><defs><marker id="arrowhead4535" viewBox="0 0 10 10" refX="9" refY="5" markerUnits="strokeWidth" markerWidth="8" markerHeight="6" orient="auto"><path d="M 0 0 L 10 5 L 0 10 z" class="arrowheadPath" style="stroke-width: 1; stroke-dasharray: 1, 0;"></path></marker></defs></g><g class="edgePath" style="opacity: 1;"><path class="path" d="M220,70L220,95L220,120" marker-end="url(#arrowhead4536)" style="stroke: #333; stroke-width: 1.5px;fill:none"></path><defs><marker id="arrowhead4536" viewBox="0 0 10 10" refX="9" refY="5" markerUnits="strokeWidth" markerWidth="8" markerHeight="6" orient="auto"><path d="M 0 0 L 10 5 L 0 10 z" class="arrowheadPath" style="stroke-width: 1; stroke-dasharray: 1, 0;"></path></marker></defs></g></g><g class="edgeLabels"><g class="edgeLabel" transform="" style="opacity: 1;"><g transform="translate(0,0)" class="label"><rect rx="0" ry="0" width="0" height="0" style="fill:#e8e8e8;"></rect><text><tspan xml:space="preserve" dy="1em" x="1"></tspan></text></g></g><g class="edgeLabel" transform="" style="opacity: 1;"><g transform="translate(0,0)" class="label"><rect rx="0" ry="0" width="0" height="0" style="fill:#e8e8e8;"></rect><text><tspan xml:space="preserve" dy="1em" x="1"></tspan></text></g></g><g class="edgeLabel" transform="" style="opacity: 1;"><g transform="translate(0,0)" class="label"><rect rx="0" ry="0" width="0" height="0" style="fill:#e8e8e8;"></rect><text><tspan xml:space="preserve" dy="1em" x="1"></tspan></text></g></g><g class="edgeLabel" transform="" style="opacity: 1;"><g transform="translate(0,0)" class="label"><rect rx="0" ry="0" width="0" height="0" style="fill:#e8e8e8;"></rect><text><tspan xml:space="preserve" dy="1em" x="1"></tspan></text></g></g><g class="edgeLabel" transform="" style="opacity: 1;"><g transform="translate(0,0)" class="label"><rect rx="0" ry="0" width="0" height="0" style="fill:#e8e8e8;"></rect><text><tspan xml:space="preserve" dy="1em" x="1"></tspan></text></g></g><g class="edgeLabel" transform="" style="opacity: 1;"><g transform="translate(0,0)" class="label"><rect rx="0" ry="0" width="0" height="0" style="fill:#e8e8e8;"></rect><text><tspan xml:space="preserve" dy="1em" x="1"></tspan></text></g></g><g class="edgeLabel" transform="" style="opacity: 1;"><g transform="translate(0,0)" class="label"><rect rx="0" ry="0" width="0" height="0" style="fill:#e8e8e8;"></rect><text><tspan xml:space="preserve" dy="1em" x="1"></tspan></text></g></g><g class="edgeLabel" transform="" style="opacity: 1;"><g transform="translate(0,0)" class="label"><rect rx="0" ry="0" width="0" height="0" style="fill:#e8e8e8;"></rect><text><tspan xml:space="preserve" dy="1em" x="1"></tspan></text></g></g><g class="edgeLabel" transform="" style="opacity: 1;"><g transform="translate(0,0)" class="label"><rect rx="0" ry="0" width="0" height="0" style="fill:#e8e8e8;"></rect><text><tspan xml:space="preserve" dy="1em" x="1"></tspan></text></g></g><g class="edgeLabel" transform="" style="opacity: 1;"><g transform="translate(0,0)" class="label"><rect rx="0" ry="0" width="0" height="0" style="fill:#e8e8e8;"></rect><text><tspan xml:space="preserve" dy="1em" x="1"></tspan></text></g></g><g class="edgeLabel" transform="" style="opacity: 1;"><g transform="translate(0,0)" class="label"><rect rx="0" ry="0" width="0" height="0" style="fill:#e8e8e8;"></rect><text><tspan xml:space="preserve" dy="1em" x="1"></tspan></text></g></g><g class="edgeLabel" transform="" style="opacity: 1;"><g transform="translate(0,0)" class="label"><rect rx="0" ry="0" width="0" height="0" style="fill:#e8e8e8;"></rect><text><tspan xml:space="preserve" dy="1em" x="1"></tspan></text></g></g><g class="edgeLabel" transform="" style="opacity: 1;"><g transform="translate(0,0)" class="label"><rect rx="0" ry="0" width="0" height="0" style="fill:#e8e8e8;"></rect><text><tspan xml:space="preserve" dy="1em" x="1"></tspan></text></g></g></g><g class="nodes"><g class="node" id="A" transform="translate(170,20)" style="opacity: 1;"><rect rx="0" ry="0" x="-10" y="-10" width="20" height="20"></rect><g class="label" transform="translate(0,0)"><g transform="translate(0,0)"><text><tspan xml:space="preserve" dy="1em" x="1">待估参数</tspan></text></g></g></g><g class="node" id="B" transform="translate(70,70)" style="opacity: 1;"><rect rx="0" ry="0" x="-10" y="-10" width="20" height="20"></rect><g class="label" transform="translate(0,0)"><g transform="translate(0,0)"><text><tspan xml:space="preserve" dy="1em" x="1">均值</tspan></text></g></g></g><g class="node" id="C" transform="translate(170,70)" style="opacity: 1;"><rect rx="0" ry="0" x="-10" y="-10" width="20" height="20"></rect><g class="label" transform="translate(0,0)"><g transform="translate(0,0)"><text><tspan xml:space="preserve" dy="1em" x="1">比例</tspan></text></g></g></g><g class="node" id="D" transform="translate(220,70)" style="opacity: 1;"><rect rx="0" ry="0" x="-10" y="-10" width="20" height="20"></rect><g class="label" transform="translate(0,0)"><g transform="translate(0,0)"><text><tspan xml:space="preserve" dy="1em" x="1">方差</tspan></text></g></g></g><g class="node" id="E" transform="translate(120,120)" style="opacity: 1;"><rect rx="0" ry="0" x="-10" y="-10" width="20" height="20"></rect><g class="label" transform="translate(0,0)"><g transform="translate(0,0)"><text><tspan xml:space="preserve" dy="1em" x="1">大样本</tspan></text></g></g></g><g class="node" id="F" transform="translate(45,120)" style="opacity: 1;"><rect rx="0" ry="0" x="-10" y="-10" width="20" height="20"></rect><g class="label" transform="translate(0,0)"><g transform="translate(0,0)"><text><tspan xml:space="preserve" dy="1em" x="1">小样本</tspan></text></g></g></g><g class="node" id="G" transform="translate(20,170)" style="opacity: 1;"><rect rx="0" ry="0" x="-10" y="-10" width="20" height="20"></rect><g class="label" transform="translate(0,0)"><g transform="translate(0,0)"><text><tspan xml:space="preserve" dy="1em" x="1">正态总体方差已知</tspan></text></g></g></g><g class="node" id="H" transform="translate(70,170)" style="opacity: 1;"><rect rx="0" ry="0" x="-10" y="-10" width="20" height="20"></rect><g class="label" transform="translate(0,0)"><g transform="translate(0,0)"><text><tspan xml:space="preserve" dy="1em" x="1">正态总体方差未知</tspan></text></g></g></g><g class="node" id="I" transform="translate(120,170)" style="opacity: 1;"><rect rx="5" ry="5" x="-10" y="-10" width="20" height="20"></rect><g class="label" transform="translate(0,0)"><g transform="translate(0,0)"><text><tspan xml:space="preserve" dy="1em" x="1">z分布</tspan></text></g></g></g><g class="node" id="J" transform="translate(20,220)" style="opacity: 1;"><rect rx="5" ry="5" x="-10" y="-10" width="20" height="20"></rect><g class="label" transform="translate(0,0)"><g transform="translate(0,0)"><text><tspan xml:space="preserve" dy="1em" x="1">z分布</tspan></text></g></g></g><g class="node" id="K" transform="translate(70,220)" style="opacity: 1;"><rect rx="5" ry="5" x="-10" y="-10" width="20" height="20"></rect><g class="label" transform="translate(0,0)"><g transform="translate(0,0)"><text><tspan xml:space="preserve" dy="1em" x="1">t分布</tspan></text></g></g></g><g class="node" id="L" transform="translate(170,120)" style="opacity: 1;"><rect rx="0" ry="0" x="-10" y="-10" width="20" height="20"></rect><g class="label" transform="translate(0,0)"><g transform="translate(0,0)"><text><tspan xml:space="preserve" dy="1em" x="1">大样本</tspan></text></g></g></g><g class="node" id="M" transform="translate(170,170)" style="opacity: 1;"><rect rx="5" ry="5" x="-10" y="-10" width="20" height="20"></rect><g class="label" transform="translate(0,0)"><g transform="translate(0,0)"><text><tspan xml:space="preserve" dy="1em" x="1">z分布</tspan></text></g></g></g><g class="node" id="N" transform="translate(220,120)" style="opacity: 1;"><rect rx="5" ry="5" x="-10" y="-10" width="20" height="20"></rect><g class="label" transform="translate(0,0)"><g transform="translate(0,0)"><text><tspan xml:space="preserve" dy="1em" x="1">卡方分布</tspan></text></g></g></g></g></g></g></svg>

两个总体参数的区间估计

总体参数符号表示样本统计量
均值之差 μ1μ2 x1x2
比例之差 π1π2 p1p2
方差比 σ22σ12 s22s12

两个总体均值之差的区间估计

1.独立大样本
条件:两个总体都服从正态分布,σ12,σ22已知
若不是正态分布,可以用正态分布来近似(n130n230)
两个样本是独立的随机样本
2.使用正态分布统计量 z
z=n1σ12+n2σ22(x1x2(μ1μ2)) N(0,1)
σ12,σ22已知时,两个总体均值之差μ1μ21α置信水平下的置信区间为(x1x2)±z2αn1σ12+n2σ22
σ12,σ22已知时,两个总体均值之差μ1μ21α置信水平下的置信区间为(x1x2)±z2αn1s12+n2s22

独立小样本(σ12=σ22)
1.假定条件
两个总体都服从正态分布
两个总体方差未知但是相等(\sigma_1^2=\sigma_2^2)
两个独立的小样本(\n_1<30和n2<30)
2.总体方差的合并估计量
sp2=n1+n22(n11)s12+(n21)s22
3.估计量x1x2的抽样标准差
n1sp2+n2sp2=spn11+n21
两个样本均值之差的标准化
t=spn11+n21(x1x2)(μ1μ2) t(n1+n22)
两个总体均值之差(μ1μ2)在1α在置信水平下的置信区间为
(x1x2)±t2α(n1+n22)sp2(n11+n21)

独立小样本(σ12σ22)
1.假定条件
两个总体都服从正态分布
两个总体方差未知且不相等,α12α22
两个独立的小样本(n1<30,n2<30)
2.使用统计量
t=n1s12+n2s22(x1x2) t(v)

两个总体均值之差(μ1μ2)在1α置信水平下的置信区间为
(x1x2)±t2α(v)n1s12+n2s22
其中v是指自由度,v=n11(n1s12)+n21(n1s22)(n1s12+n2s22)
匹配大样本
1.假定条件
两个匹配的大样本(n130n230)
两个总体各观察值的配对差服从正态分布
2.两个总体均值之差(μd=μ1μ21α)置信水平下的置信区间
d±z2αnσd
匹配小样本
1.假定条件
两个匹配的小样本(n1<30n2<30)
两个总体各观察值的配对差服从正态分布
两个总体均值之差(μd=μ1μ2)在1α置信水平下的置信区间为d±t2α(n1)nsd

两个总体比例之差的区间估计

1.假定条件
两个总体服从二项分布
可以用正态分布来近似
两个样本是独立的
2.两个总体比例之差π1π21α置信水平下的置信区间为
(p1p2)±z2αn1p1(1p1)+n2p2(1p2)

两个总体方差比的区间估计

1.比较两个总体的方差比
2.用两个样本的方差比来判断

  • 如果S22S12接近于1,说明两个总体方差很接近
  • 如果S22S12远离1,说明两个总体方差之间存在差异
    3.总体方差比在1α置信水平下的置信区间
    \frac{\frac{s_1^2}{s_2^2}}{F_{\frac{\alpha}{2}}} \leq \frac{\sigma_1^2}{\sigma_2^2} \leq \frac{\frac{s_1^2}{s_2^2}}{F_{1-\frac{\alpha}{2}}

样本容量的确定

估计总体均值时样本容量的确定

1.估计总体均值时样本容量n为
n=E2z2α2σ2
2.样本容量n与总体方差σ2,边际误差E和可靠性系数Z或t之间的关系为

  • 与总体方差成正比
  • 与边际误差成反比
  • 与可靠性系数成正比

估计总体比例时样本容量的确定

1.根据比例区间估计公式可得样本容量
n=E2(zfracα2)2 dotπ(1π)
其中 E=z2αnπ(1π)
2.E的取值一般小于0.1
3.π未知时,可取最大值0.5

估计两个总体均值之差时样本容量

1.设n1n2来自两个总体的样本,并假定n1=n2
2.根据均值之差的区间估计公式可得两个样本的容量n为
n1=n2=n=E2(z2α)(σ12+σ22)
其中E=z2αnσ1+σ2

估计两个总体比例之差时样本容量

1.设n1n2来自两个总体的样本,并假定n1=n2
2.根据比例之差的区间估计公式可得两个样本的容量n为
n1=n2=n=E2(zfracα2)2[π1(1π1)+π2(1π2)]
其中E=z2αnπ1(1π1)+π2(1π2)

%23%23%23%20%E5%8F%82%E6%95%B0%E4%BC%B0%E8%AE%A1%E7%9A%84%E5%9F%BA%E6%9C%AC%E5%8E%9F%E7%90%86%0A%23%23%23%20%E4%B8%80%E4%B8%AA%E6%80%BB%E4%BD%93%E5%8F%82%E6%95%B0%E7%9A%84%E5%8C%BA%E9%97%B4%E4%BC%B0%E8%AE%A1%0A%23%23%23%20%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E5%8F%82%E6%95%B0%E7%9A%84%E5%8C%BA%E9%97%B4%E4%BC%B0%E8%AE%A1%0A%23%23%23%20%E6%A0%B7%E6%9C%AC%E5%AE%B9%E9%87%8F%E7%9A%84%E7%A1%AE%E5%AE%9A%0A%0A%3E%E6%8E%8C%E6%8F%A1%E7%9B%AE%E6%A0%87%0A%3E%E4%BC%B0%E8%AE%A1%E9%87%8F%E4%B8%8E%E4%BC%B0%E8%AE%A1%E5%80%BC%E7%9A%84%E6%A6%82%E5%BF%B5%0A%3E%E7%82%B9%E4%BC%B0%E8%AE%A1%E4%B8%8E%E5%8C%BA%E9%97%B4%E4%BC%B0%E8%AE%A1%E7%9A%84%E5%8C%BA%E5%88%AB%0A%3E%E8%AF%84%E4%BB%B7%E4%BC%B0%E8%AE%A1%E9%87%8F%E4%BC%98%E8%89%AF%E6%80%A7%E7%9A%84%E6%A0%87%E5%87%86%0A%3E%E4%B8%80%E4%B8%AA%E6%80%BB%E4%BD%93%E5%8F%82%E6%95%B0%E7%9A%84%E5%8C%BA%E9%97%B4%E4%BC%B0%E8%AE%A1%E6%96%B9%E6%B3%95%0A%3E%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E5%8F%82%E6%95%B0%E7%9A%84%E5%8C%BA%E9%97%B4%E4%BC%B0%E8%AE%A1%E6%96%B9%E6%B3%95%0A%3E%E6%A0%B7%E6%9C%AC%E5%AE%B9%E9%87%8F%E7%9A%84%E7%A1%AE%E5%AE%9A%E6%96%B9%E6%B3%95%0A%0A%60%60%60mermaid%0Agraph%20TD%0AA%5B%E7%BB%9F%E8%AE%A1%E6%96%B9%E6%B3%95%5D%20--%3EB(%E6%8F%8F%E8%BF%B0%E7%BB%9F%E8%AE%A1)%0AA%5B%E7%BB%9F%E8%AE%A1%E6%96%B9%E6%B3%95%5D%20--%3EC(%E6%8E%A8%E6%96%AD%E7%BB%9F%E8%AE%A1)%0AC%5B%E6%8E%A8%E6%96%AD%E7%BB%9F%E8%AE%A1%5D%20--%3ED(%E5%8F%82%E6%95%B0%E4%BC%B0%E8%AE%A1)%0AC%5B%E6%8E%A8%E6%96%AD%E7%BB%9F%E8%AE%A1%5D%20--%3EE(%E5%81%87%E8%AE%BE%E6%A3%80%E9%AA%8C)%0A%60%60%60%0A%0A%23%23%23%23%20%E4%BC%B0%E8%AE%A1%E9%87%8F%E4%B8%8E%E4%BC%B0%E8%AE%A1%E5%80%BC%0A%3E1.%E4%BC%B0%E8%AE%A1%E9%87%8F%EF%BC%9A%E7%94%A8%E4%BA%8E%E4%BC%B0%E8%AE%A1%E6%80%BB%E4%BD%93%E5%8F%82%E6%95%B0%E7%9A%84%E9%9A%8F%E6%9C%BA%E5%8F%98%E9%87%8F%EF%BC%8C%E5%A6%82%E6%A0%B7%E6%9C%AC%E5%9D%87%E5%80%BC%EF%BC%8C%E6%A0%B7%E6%9C%AC%E6%AF%94%E4%BE%8B%EF%BC%8C%E6%A0%B7%E6%9C%AC%E6%96%B9%E5%B7%AE%EF%BC%8C%E4%BE%8B%E5%A6%82%EF%BC%9A%E6%A0%B7%E6%9C%AC%E5%9D%87%E5%80%BC%E5%B0%B1%E6%98%AF%E6%80%BB%E4%BD%93%E5%9D%87%E5%80%BC%E4%B8%AD%E7%9A%84%E4%B8%80%E4%B8%AA%E4%BC%B0%E8%AE%A1%E9%87%8F%0A%3E2.%E5%8F%82%E6%95%B0%E7%94%A8%24%5Ctheta%24%E8%A1%A8%E7%A4%BA%EF%BC%8C%E4%BC%B0%E8%AE%A1%E9%87%8F%E4%BD%BF%E7%94%A8%24%5Chat%7B%5Ctheta%7D%24%E8%A1%A8%E7%A4%BA%0A%3E3.%E4%BC%B0%E8%AE%A1%E5%80%BC%EF%BC%9A%E4%BC%B0%E8%AE%A1%E5%8F%82%E6%95%B0%E6%97%B6%E8%AE%A1%E7%AE%97%E5%87%BA%E6%9D%A5%E7%9A%84%E7%BB%9F%E8%AE%A1%E9%87%8F%E7%9A%84%E6%80%BB%E4%BD%93%E5%80%BC%EF%BC%8C%E5%A6%82%E6%9E%9C%E6%A0%B7%E6%9C%AC%E5%9D%87%E5%80%BC%E4%B8%BA%24%5Coverline%7Bx%7D%3D80%24%2C%E5%88%9980%E5%B0%B1%E6%98%AF%E4%BC%B0%E8%AE%A1%E5%80%BC%0A%0A%23%23%23%23%20%E7%82%B9%E4%BC%B0%E8%AE%A1%E4%B8%8E%E5%8C%BA%E9%97%B4%E4%BC%B0%E8%AE%A1%0A%0A%60%60%60mermaid%0Agraph%20TD%0AA%5B%E4%BC%B0%E8%AE%A1%E6%96%B9%E6%B3%95%5D%20--%3EB(%E7%82%B9%E4%BC%B0%E8%AE%A1)%0AA%5B%E4%BC%B0%E8%AE%A1%E6%96%B9%E6%B3%95%5D%20--%3EC(%E5%8C%BA%E9%97%B4%E4%BC%B0%E8%AE%A1)%0AB%5B%E7%82%B9%E4%BC%B0%E8%AE%A1%5D%20--%3E%20D(%E7%9F%A9%E4%BC%B0%E8%AE%A1%E6%B3%95)%0AB%5B%E7%82%B9%E4%BC%B0%E8%AE%A1%5D%20--%3E%20E(%E9%A1%BA%E5%BA%8F%E7%BB%9F%E8%AE%A1%E9%87%8F%E6%B3%95)%0AB%5B%E7%82%B9%E4%BC%B0%E8%AE%A1%5D%20--%3E%20F(%E6%9C%80%E5%A4%A7%E4%BC%BC%E7%84%B6%E6%B3%95)%0AB%5B%E7%82%B9%E4%BC%B0%E8%AE%A1%5D%20--%3E%20G(%E6%9C%80%E5%B0%8F%E4%BA%8C%E4%B9%98%E6%B3%95)%0A%60%60%60%0A%3E%E7%82%B9%E4%BC%B0%E8%AE%A1%EF%BC%9A%E7%94%A8%E6%A0%B7%E6%9C%AC%E7%9A%84%E4%BC%B0%E8%AE%A1%E9%87%8F%E7%9B%B4%E6%8E%A5%E4%BD%9C%E4%B8%BA%E6%80%BB%E4%BD%93%E5%8F%82%E6%95%B0%E7%9A%84%E4%BC%B0%E8%AE%A1%E5%80%BC%EF%BC%8C%E7%94%A8%E6%A0%B7%E6%9C%AC%E5%9D%87%E5%80%BC%E7%9B%B4%E6%8E%A5%E4%BD%9C%E4%B8%BA%E6%80%BB%E4%BD%93%E5%9D%87%E5%80%BC%E7%9A%84%E4%BC%B0%E8%AE%A1%0A%3E%E7%94%A8%E4%B8%A4%E4%B8%AA%E6%A0%B7%E6%9C%AC%E5%9D%87%E5%80%BC%E4%B9%8B%E5%B7%AE%E7%9B%B4%E6%8E%A5%E4%BD%9C%E4%B8%BA%E6%80%BB%E4%BD%93%E5%9D%87%E5%80%BC%E4%B9%8B%E5%B7%AE%E7%9A%84%E4%BC%B0%E8%AE%A1%0A%3E%E6%B2%A1%E6%9C%89%E7%BB%99%E5%87%BA%E4%BC%B0%E8%AE%A1%E5%80%BC%E6%8E%A5%E8%BF%91%E6%80%BB%E4%BD%93%E5%8F%82%E6%95%B0%E7%A8%8B%E5%BA%A6%E7%9A%84%E4%BF%A1%E6%81%AF%0A%0A%3E%E5%8C%BA%E9%97%B4%E4%BC%B0%E8%AE%A1%EF%BC%9A%E5%9C%A8%E7%82%B9%E4%BC%B0%E8%AE%A1%E7%9A%84%E6%80%BB%E4%BD%93%E5%9F%BA%E7%A1%80%E4%B8%8A%EF%BC%8C%E7%BB%99%E5%87%BA%E6%80%BB%E4%BD%93%E5%8F%82%E6%95%B0%E4%BC%B0%E8%AE%A1%E7%9A%84%E4%B8%80%E4%B8%AA%E5%8C%BA%E9%97%B4%E8%8C%83%E5%9B%B4%EF%BC%8C%E8%AF%A5%E5%8C%BA%E9%97%B4%E7%94%B1%E6%A0%B7%E6%9C%AC%E7%BB%9F%E8%AE%A1%E9%87%8F%E5%8A%A0%E5%87%8F%E6%8A%BD%E6%A0%B7%E8%AF%AF%E5%B7%AE%E8%80%8C%E5%BE%97%E5%88%B0%E7%9A%84%E3%80%82%0A%3E%E6%A0%B9%E6%8D%AE%E6%A0%B7%E6%9C%AC%E7%BB%9F%E8%AE%A1%E9%87%8F%E7%9A%84%E6%8A%BD%E6%A0%B7%E5%88%86%E5%B8%83%E8%83%BD%E5%A4%9F%E5%AF%B9%E6%A0%B7%E6%9C%AC%E7%BB%9F%E8%AE%A1%E9%87%8F%E4%B8%8E%E6%80%BB%E4%BD%93%E5%8F%82%E6%95%B0%E7%9A%84%E6%8E%A5%E8%BF%91%E7%A8%8B%E5%BA%A6%E7%BB%99%E5%87%BA%E4%B8%80%E4%B8%AA%E6%A6%82%E7%8E%87%E7%BB%9F%E8%AE%A1%E9%87%8F%EF%BC%8C%E6%AF%94%E5%A6%82%E6%9F%90%E7%8F%AD%E7%BA%A7%E5%B9%B3%E5%9D%87%E5%88%86%E6%95%B0%E5%9C%A875-85%E5%88%86%E4%B9%8B%E9%97%B4%EF%BC%8C%20%E7%BD%AE%E4%BF%A1%E6%B0%B4%E5%B9%B3%E6%98%AF95%25%0A%3E**%E7%BD%AE%E4%BF%A1%E6%B0%B4%E5%B9%B3**%EF%BC%9A%E5%B0%86%E6%9E%84%E9%80%A0%E7%BD%AE%E4%BF%A1%E5%8C%BA%E9%97%B4%E7%9A%84%E6%AD%A5%E9%AA%A4%E9%87%8D%E5%A4%8D%E5%BE%88%E5%A4%9A%E6%AC%A1%EF%BC%8C%E7%BD%AE%E4%BF%A1%E5%8C%BA%E9%97%B4%E5%8C%85%E5%90%AB%E6%80%BB%E4%BD%93%E5%8F%82%E6%95%B0%E7%9C%9F%E5%80%BC%E7%9A%84%E6%AC%A1%E6%95%B0%E6%89%80%E5%8D%A0%E7%9A%84%E6%AF%94%E4%BE%8B%E7%A7%B0%E4%B8%BA%E7%BD%AE%E4%BF%A1%E6%B0%B4%E5%B9%B3%0A%3E%E5%B8%B8%E7%94%A8%E7%9A%84%E7%BD%AE%E4%BF%A1%E6%B0%B4%E5%B9%B3%E6%9C%8999%25%EF%BC%8C95%25%EF%BC%8C90%25%0A%3E%E7%94%B1%E6%A0%B7%E6%9C%AC%E7%BB%9F%E8%AE%A1%E9%87%8F%E6%89%80%E6%9E%84%E9%80%A0%E7%9A%84%E6%80%BB%E4%BD%93%E5%8F%82%E6%95%B0%E7%9A%84%E4%BC%B0%E8%AE%A1%E5%8C%BA%E9%97%B4%E7%A7%B0%E4%B8%BA%E7%BD%AE%E4%BF%A1%E5%8C%BA%E9%97%B4%0A%3E%E7%BB%9F%E8%AE%A1%E5%AD%A6%E5%AE%B6%E5%9C%A8%E6%9F%90%E7%A7%8D%E7%A8%8B%E5%BA%A6%E4%B8%8A%E7%A1%AE%E4%BF%A1%E8%BF%99%E4%B8%AA%E5%8C%BA%E9%97%B4%E4%BC%9A%E5%8C%85%E5%90%AB%E7%9C%9F%E6%AD%A3%E7%9A%84%E6%80%BB%E4%BD%93%E5%8F%82%E6%95%B0%EF%BC%8C%E6%89%80%E4%BB%A5%E7%BB%99%E5%AE%83%E5%8F%96%E5%90%8D%E4%B8%BA%E7%BD%AE%E4%BF%A1%E5%8C%BA%E9%97%B4%0A%3E%E7%94%A8%E4%B8%80%E4%B8%AA%E5%85%B7%E4%BD%93%E7%9A%84%E6%A0%B7%E6%9C%AC%E6%89%80%E6%9E%84%E9%80%A0%E7%9A%84%E5%8C%BA%E9%97%B4%E6%98%AF%E4%B8%80%E4%B8%AA%E7%89%B9%E5%AE%9A%E7%9A%84%E5%8C%BA%E9%97%B4%EF%BC%8C%E6%97%A0%E6%B3%95%E7%9F%A5%E9%81%93%E8%BF%99%E4%B8%AA%E6%A0%B7%E6%9C%AC%E6%89%80%E4%BA%A7%E7%94%9F%E7%9A%84%E5%8C%BA%E9%97%B4%E6%98%AF%E5%90%A6%E5%8C%85%E5%90%AB%E6%80%BB%E4%BD%93%E5%8F%82%E6%95%B0%E7%9A%84%E7%9C%9F%E5%80%BC%E3%80%82%E5%8F%AA%E8%83%BD%E6%98%AF%E5%B8%8C%E6%9C%9B%E8%BF%99%E4%B8%AA%E5%8C%BA%E9%97%B4%E6%98%AF%E5%A4%A7%E9%87%8F%E5%8C%85%E5%90%AB%E6%80%BB%E4%BD%93%E5%8F%82%E6%95%B0%E7%9C%9F%E5%80%BC%E7%9A%84%E5%8C%BA%E9%97%B4%E4%B8%AD%E7%9A%84%E4%B8%80%E4%B8%AA%EF%BC%8C%E4%BD%86%E6%98%AF%E5%AE%83%E4%B9%9F%E5%8F%AF%E8%83%BD%E6%98%AF%E5%B0%91%E6%95%B0%E5%87%A0%E4%B8%AA%E4%B8%8D%E5%8C%85%E5%90%AB%E5%8F%82%E6%95%B0%E7%9C%9F%E5%80%BC%E7%9A%84%E5%8C%BA%E9%97%B4%E4%B8%AD%E7%9A%84%E4%B8%80%E4%B8%AA%E3%80%82%0A%0A%23%23%23%23%20%E8%AF%84%E4%BB%B7%E4%BC%B0%E8%AE%A1%E9%87%8F%E7%9A%84%E6%A0%87%E5%87%86---%E6%97%A0%E5%81%8F%E6%80%A7%0A%3E**%E6%97%A0%E5%81%8F%E6%80%A7**%E4%BC%B0%E8%AE%A1%E9%87%8F%E6%8A%BD%E6%A0%B7%E5%88%86%E5%B8%83%E7%9A%84%E6%95%B0%E5%AD%A6%E6%9C%9F%E6%9C%9B%E7%AD%89%E4%BA%8E%E8%A2%AB%E4%BC%B0%E8%AE%A1%E7%9A%84%E6%80%BB%E4%BD%93%E5%8F%82%E6%95%B0%0A%3E**%E6%9C%89%E6%95%88%E6%80%A7**%E5%AF%B9%E5%90%8C%E4%B8%80%E6%80%BB%E4%BD%93%E5%8F%82%E6%95%B0%E7%9A%84%E4%B8%A4%E4%B8%AA%E6%97%A0%E5%81%8F%E7%82%B9%E4%BC%B0%E8%AE%A1%E9%87%8F%EF%BC%8C%E6%9C%89%E6%9B%B4%E5%B0%8F%E6%A0%87%E5%87%86%E5%B7%AE%E7%9A%84%E4%BC%B0%E8%AE%A1%E9%87%8F%E6%9B%B4%E6%9C%89%E6%95%88%0A%3E**%E4%B8%80%E8%87%B4%E6%80%A7**%E9%9A%8F%E7%9D%80%E6%A0%B7%E6%9C%AC%E5%AE%B9%E9%87%8F%E7%9A%84%E5%A2%9E%E5%A4%A7%EF%BC%8C%E4%BC%B0%E8%AE%A1%E9%87%8F%E7%9A%84%E5%80%BC%E8%B6%8A%E6%9D%A5%E8%B6%8A%E6%8E%A5%E8%BF%91%E8%A2%AB%E4%BC%B0%E8%AE%A1%E7%9A%84%E6%80%BB%E4%BD%93%E5%8F%82%E6%95%B0%0A%0A%23%23%23%20%E4%B8%80%E4%B8%AA%E6%80%BB%E4%BD%93%E5%8F%82%E6%95%B0%E7%9A%84%E5%8C%BA%E9%97%B4%E4%BC%B0%E8%AE%A1%0A%0A%7C%20%E6%80%BB%E4%BD%93%E5%8F%82%E6%95%B0%20%7C%E7%AC%A6%E5%8F%B7%E8%A1%A8%E7%A4%BA%20%20%7C%E6%A0%B7%E6%9C%AC%E7%BB%9F%E8%AE%A1%E9%87%8F%20%20%7C%0A%7C%20---%20%7C%20---%20%7C%20---%20%7C%0A%7C%20**%E5%9D%87%E5%80%BC**%20%7C%20%24%5Cmu%24%20%7C%20%24%5Coverline%7Bx%7D%24%20%7C%0A%7C%20**%E6%AF%94%E4%BE%8B**%20%7C%20%24%5Cpi%24%20%7C%20%24P%24%20%7C%0A%7C%20**%E6%96%B9%E5%B7%AE**%20%7C%20%24%5Csigma%5E2%24%20%7C%20%24s%5E2%24%20%7C%0A%0A%23%23%23%23%20%E6%80%BB%E4%BD%93%E5%9D%87%E5%80%BC%E7%9A%84%E5%8C%BA%E9%97%B4%E4%BC%B0%E8%AE%A1%0A%3E%E6%AD%A3%E6%80%81%E6%80%BB%E4%BD%93%E3%80%81%24%5Csigma%5E2%24%E5%B7%B2%E7%9F%A5%EF%BC%8C%E6%88%96%E9%9D%9E%E6%AD%A3%E6%80%81%E6%80%BB%E4%BD%93%E3%80%81%E5%A4%A7%E6%A0%B7%E6%9C%AC%0A%3E%E5%81%87%E5%AE%9A%E6%9D%A1%E4%BB%B6%EF%BC%9A%E6%80%BB%E4%BD%93%E6%9C%8D%E4%BB%8E%E6%AD%A3%E6%80%81%E5%88%86%E5%B8%83%EF%BC%8C%E4%B8%94%E6%96%B9%E5%B7%AE(%24%5Csigma%5E2%24)%E5%B7%B2%E7%9F%A5%0A%3E%E5%A6%82%E6%9E%9C%E4%B8%8D%E6%98%AF%E6%AD%A3%E6%80%81%E5%88%86%E5%B8%83%EF%BC%8C%E5%8F%AF%E7%94%B1%E6%AD%A3%E6%80%81%E5%88%86%E5%B8%83%E6%9D%A5%E8%BF%91%E4%BC%BC(%E5%A4%A7%E6%A0%B7%E6%9C%ACn%3E%3D30)%0A%3E%E4%BD%BF%E7%94%A8%E6%AD%A3%E6%80%81%E5%88%86%E5%B8%83%E7%BB%9F%E8%AE%A1%E9%87%8Fz%0A%3E%E6%80%BB%E4%BD%93%E5%9D%87%E5%80%BC%24%5Cmu%24%E5%9C%A8%241-%5Calpha%24%E7%9A%84%E7%BD%AE%E4%BF%A1%E6%B0%B4%E5%B9%B3%E4%B8%8B%E7%9A%84%E5%85%AC%E5%BC%8F%E4%B8%BA%0A%3E%24%5Coverline%7Bx%7D%20%5Cpm%20z_%7B%5Cfrac%7B%5Calpha%7D%7B2%7D%7D%24%0A%3E%E6%88%96%24%5Coverline%7Bx%7D%20%5Cpm%20z_%7B%5Cfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%7D%7D%24(%24%5Calpha%24%E6%9C%AA%E7%9F%A5)%0A%0A-------------%0A%3E**%E6%AD%A3%E6%80%81%E6%80%BB%E4%BD%93%E3%80%81%24%5Csigma%5E2%24%E6%9C%AA%E7%9F%A5%E3%80%81%E5%B0%8F%E6%A0%B7%E6%9C%AC**%0A%3E1.%E5%81%87%E5%AE%9A%E6%9D%A1%E4%BB%B6%0A%3E%20-%20%E6%80%BB%E4%BD%93%E6%9C%8D%E4%BB%8E%E6%AD%A3%E6%80%81%E5%88%86%E5%B8%83%EF%BC%8C%E4%B8%94%E6%96%B9%E5%B7%AE(%24%5Csigma%5E2%24)%E6%9C%AA%E7%9F%A5%0A%3E%20-%20%E5%B0%8F%E6%A0%B7%E6%9C%AC(n%3C30)%0A%3E2.%E4%BD%BF%E7%94%A8t%E5%88%86%E5%B8%83%E7%BB%9F%E8%AE%A1%E9%87%8F%0A%3E%24t%3D%5Cfrac%7B%5Coverline%7Bx%7D-%5Cmu%7D%7B%5Cfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%7D%7D~t(n-1)%24%0A%3E3.%E6%80%BB%E4%BD%93%E5%9D%87%E5%80%BC%24%5Cmu%24%E5%9C%A8%241-%5Calpha%24%E7%BD%AE%E4%BF%A1%E6%B0%B4%E5%B9%B3%E4%B8%8B%E7%9A%84%E7%BD%AE%E4%BF%A1%E5%8C%BA%E9%97%B4%0A%3E%24%5Coverline%7Bx%7D%20%5Cpm%20t_%7B%5Cfrac%7B%5Calpha%7D%7B2%7D%7D%5Cfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%7D%24%0A%3E**t%E5%88%86%E5%B8%83**t%E5%88%86%E5%B8%83%E5%BC%8F%E7%B1%BB%E4%BC%BC%E6%AD%A3%E6%80%81%E5%88%86%E5%B8%83%E7%9A%84%E4%B8%80%E7%A7%8D%E5%AF%B9%E7%A7%B0%E5%88%86%E5%B8%83%EF%BC%8C%E5%AE%83%E9%80%9A%E5%B8%B8%E8%A6%81%E6%AF%94%E6%AD%A3%E6%80%81%E5%88%86%E5%B8%83%E5%B9%B3%E5%9D%A6%E5%92%8C%E5%88%86%E6%95%A3%EF%BC%8C%E4%B8%80%E4%B8%AA%E7%89%B9%E5%AE%9A%E7%9A%84%E5%88%86%E5%B8%83%E4%BE%9D%E8%B5%96%E4%BA%8E%E7%A7%B0%E4%B9%8B%E4%B8%BA%E8%87%AA%E7%94%B1%E5%BA%A6%E7%9A%84%E5%8F%82%E6%95%B0%EF%BC%8C%E9%9A%8F%E7%9D%80%E8%87%AA%E7%94%B1%E5%BA%A6%E7%9A%84%E5%A2%9E%E5%A4%A7%EF%BC%8C%E5%88%86%E5%B8%83%E6%9B%B4%E8%B6%8B%E5%90%91%E4%BA%8E%E6%AD%A3%E6%80%81%E5%88%86%E5%B8%83%E3%80%82%0A%0A%23%23%23%23%20%E6%80%BB%E4%BD%93%E6%AF%94%E4%BE%8B%E7%9A%84%E5%8C%BA%E9%97%B4%E4%BC%B0%E8%AE%A1%0A%3E%201.%E5%81%87%E5%AE%9A%E6%9D%A1%E4%BB%B6%0A%3E%20-%20%E6%80%BB%E4%BD%93%E6%9C%8D%E4%BB%8E%E4%BA%8C%E9%A1%B9%E5%88%86%E5%B8%83%0A%3E%20-%20%E5%8F%AF%E4%BB%A5%E7%94%B1%E6%AD%A3%E6%80%81%E5%88%86%E5%B8%83%E6%9D%A5%E8%BF%91%E4%BC%BC%0A%3E%202.%E4%BD%BF%E7%94%A8%E6%AD%A3%E6%80%81%E5%88%86%E5%B8%83%E7%BB%9F%E8%AE%A1%E9%87%8F%20Z%0A%3E%20%24z%3D%5Cfrac%7Bp-%5Cpi%7D%7B%5Csqrt%7B%5Cfrac%7B%5Cpi(1-%5Cpi)%7D%7Bn%7D%7D%7D~N(0%2C1)%24%0A%3E%203.%E6%80%BB%E4%BD%93%E6%AF%94%E4%BE%8B%24%5Cpi%24%E5%9C%A8%241-%5Calpha%24%E7%BD%AE%E4%BF%A1%E6%B0%B4%E5%B9%B3%E4%B8%8B%E7%9A%84%E7%BD%AE%E4%BF%A1%E5%8C%BA%E9%97%B4%0A%3E%20%24p%20%5Cpm%20z_%7B%5Cfrac%7B%5Calpha%7D%7B2%7D%7D%5Csqrt%7B%5Cfrac%7B%5Cpi(1-%5Cpi)%7D%7Bn%7D%7D%24%E6%88%96%24p%20%5Cpm%20z_%7B%5Cfrac%7B%5Calpha%7D%7B2%7D%7D%5Csqrt%7B%5Cfrac%7Bp(1-p)%7D%7Bn%7D%7D%24%2C%24%5Cpi%24%E6%9C%AA%E7%9F%A5%E6%97%B6%0A%0A%23%23%23%23%20%E6%80%BB%E4%BD%93%E6%96%B9%E5%B7%AE%E7%9A%84%E5%8C%BA%E9%97%B4%E4%BC%B0%E8%AE%A1%0A%3E1.%E4%BC%B0%E8%AE%A1%E4%B8%80%E4%B8%AA%E6%80%BB%E4%BD%93%E7%9A%84%E6%96%B9%E5%B7%AE%E6%88%96%E6%A0%87%E5%87%86%E5%B7%AE%0A%3E2.%E5%81%87%E8%AE%BE%E6%80%BB%E4%BD%93%E6%9C%8D%E4%BB%8E%E6%AD%A3%E6%80%81%E5%88%86%E5%B8%83%0A%3E3.%E6%80%BB%E4%BD%93%E6%96%B9%E5%B7%AE%E7%9A%84%E7%82%B9%E4%BC%B0%E8%AE%A1%E9%87%8F%E4%B8%BA%24s%5E2%24%2C%E4%B8%94%24%5Cfrac%7B(n-1)s%5E2%7D%7B%5Csigma%5E2%7D~%5Cchi%5E2(n-1)%24%0A%3E4.%E6%80%BB%E4%BD%93%E6%96%B9%E5%B7%AE%E5%9C%A8%241-%5Calpha%24%E7%BD%AE%E4%BF%A1%E6%B0%B4%E5%B9%B3%E4%B8%8B%E7%9A%84%E7%BD%AE%E4%BF%A1%E5%8C%BA%E9%97%B4%E4%B8%BA%24%5Cfrac%7B(n-1)s%5E2%7D%7B%5Cchi%5E2_%7B%5Cfrac%7B%5Calpha%7D%7B2%7D%7D(n-1)%7D%24%3C%3D%24%5Csigma%5E2%24%3C%3D%24%5Cfrac%7B(n-1)s%5E2%7D%7B%5Cchi%5E2_1%7B%5Cfrac%7B%5Calpha%7D%7B2%7D%7D(n-1)%7D%24%0A%0A%60%60%60mermaid%0Agraph%20TD%0AA%5B%E5%BE%85%E4%BC%B0%E5%8F%82%E6%95%B0%5D%20--%3EB(%E5%9D%87%E5%80%BC)%0AA%5B%E5%BE%85%E4%BC%B0%E5%8F%82%E6%95%B0%5D%20--%3EC(%E6%AF%94%E4%BE%8B)%0AA%5B%E5%BE%85%E4%BC%B0%E5%8F%82%E6%95%B0%5D%20--%3ED(%E6%96%B9%E5%B7%AE)%0AB%5B%E5%9D%87%E5%80%BC%5D%20--%3E%20E(%E5%A4%A7%E6%A0%B7%E6%9C%AC)%0AB%5B%E5%9D%87%E5%80%BC%5D%20--%3E%20F(%E5%B0%8F%E6%A0%B7%E6%9C%AC)%0AF%5B%E5%B0%8F%E6%A0%B7%E6%9C%AC%5D%20--%3E%20G(%E6%AD%A3%E6%80%81%E6%80%BB%E4%BD%93%E6%96%B9%E5%B7%AE%E5%B7%B2%E7%9F%A5)%0AF%5B%E5%B0%8F%E6%A0%B7%E6%9C%AC%5D%20--%3E%20H(%E6%AD%A3%E6%80%81%E6%80%BB%E4%BD%93%E6%96%B9%E5%B7%AE%E6%9C%AA%E7%9F%A5)%0AE%5B%E5%A4%A7%E6%A0%B7%E6%9C%AC%5D%20--%3E%20I(z%E5%88%86%E5%B8%83)%0A%20G%5B%E6%AD%A3%E6%80%81%E6%80%BB%E4%BD%93%E6%96%B9%E5%B7%AE%E5%B7%B2%E7%9F%A5%5D%20--%3E%20J(z%E5%88%86%E5%B8%83)%0A%20H%5B%E6%AD%A3%E6%80%81%E6%80%BB%E4%BD%93%E6%96%B9%E5%B7%AE%E6%9C%AA%E7%9F%A5%5D%20--%3E%20K(t%E5%88%86%E5%B8%83)%0A%20C%5B%E6%AF%94%E4%BE%8B%5D%20--%3E%20L(%E5%A4%A7%E6%A0%B7%E6%9C%AC)%0A%20L%5B%E5%A4%A7%E6%A0%B7%E6%9C%AC%5D%20--%3E%20M(z%E5%88%86%E5%B8%83)%0A%20D%5B%E6%96%B9%E5%B7%AE%5D%20--%3E%20N(%E5%8D%A1%E6%96%B9%E5%88%86%E5%B8%83)%0A%60%60%60%0A%0A%23%23%23%20%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E5%8F%82%E6%95%B0%E7%9A%84%E5%8C%BA%E9%97%B4%E4%BC%B0%E8%AE%A1%0A%0A%7C%20%E6%80%BB%E4%BD%93%E5%8F%82%E6%95%B0%20%7C%20%E7%AC%A6%E5%8F%B7%E8%A1%A8%E7%A4%BA%20%7C%20%E6%A0%B7%E6%9C%AC%E7%BB%9F%E8%AE%A1%E9%87%8F%20%7C%0A%7C%20%3A---%3A%20%7C%20%3A---%3A%20%7C%20%3A---%3A%20%7C%0A%7C%20%E5%9D%87%E5%80%BC%E4%B9%8B%E5%B7%AE%20%7C%20%24%5Cmu_1-%5Cmu_2%24%20%7C%20%24%5Coverline%7Bx_1%7D-%5Coverline%7Bx_2%7D%24%20%7C%0A%7C%20%E6%AF%94%E4%BE%8B%E4%B9%8B%E5%B7%AE%20%7C%20%24%5Cpi_1-%5Cpi_2%24%20%7C%20%24p_1-p_2%24%20%7C%0A%7C%20%E6%96%B9%E5%B7%AE%E6%AF%94%20%7C%20%24%5Cfrac%7B%5Csigma_1%5E2%7D%7B%5Csigma_2%5E2%7D%24%20%7C%20%24%5Cfrac%7Bs_1%5E2%7D%7Bs_2%5E2%7D%24%20%7C%0A%23%23%23%23%20%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E5%9D%87%E5%80%BC%E4%B9%8B%E5%B7%AE%E7%9A%84%E5%8C%BA%E9%97%B4%E4%BC%B0%E8%AE%A1%0A%3E1.%E7%8B%AC%E7%AB%8B%E5%A4%A7%E6%A0%B7%E6%9C%AC%0A%3E%E6%9D%A1%E4%BB%B6%EF%BC%9A%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E9%83%BD%E6%9C%8D%E4%BB%8E%E6%AD%A3%E6%80%81%E5%88%86%E5%B8%83%EF%BC%8C%24%5Csigma_1%5E2%2C%5Csigma_2%5E2%24%E5%B7%B2%E7%9F%A5%0A%3E%E8%8B%A5%E4%B8%8D%E6%98%AF%E6%AD%A3%E6%80%81%E5%88%86%E5%B8%83%EF%BC%8C%E5%8F%AF%E4%BB%A5%E7%94%A8%E6%AD%A3%E6%80%81%E5%88%86%E5%B8%83%E6%9D%A5%E8%BF%91%E4%BC%BC(%24n_1%20%5Cgeq%2030%24%20%E5%92%8C%20%20%24n_2%20%5Cgeq%2030%24)%0A%3E%E4%B8%A4%E4%B8%AA%E6%A0%B7%E6%9C%AC%E6%98%AF%E7%8B%AC%E7%AB%8B%E7%9A%84%E9%9A%8F%E6%9C%BA%E6%A0%B7%E6%9C%AC%0A%3E2.%E4%BD%BF%E7%94%A8%E6%AD%A3%E6%80%81%E5%88%86%E5%B8%83%E7%BB%9F%E8%AE%A1%E9%87%8F%20z%0A%3E%24z%3D%5Cfrac%7B(%5Coverline%7Bx_1%7D-%5Coverline%7Bx_2%7D-(%5Cmu_1-%5Cmu_2))%7D%7B%5Csqrt%7B%5Cfrac%7B%5Csigma_1%5E2%7D%7Bn_1%7D%2B%5Cfrac%7B%5Csigma_2%5E2%7D%7Bn_2%7D%7D%7D~N(0%2C1)%24%0A%3E%24%5Csigma_1%5E2%2C%5Csigma_2%5E2%24%E5%B7%B2%E7%9F%A5%E6%97%B6%EF%BC%8C%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E5%9D%87%E5%80%BC%E4%B9%8B%E5%B7%AE%24%5Cmu_1-%5Cmu_2%24%E5%9C%A8%241-%5Calpha%24%E7%BD%AE%E4%BF%A1%E6%B0%B4%E5%B9%B3%E4%B8%8B%E7%9A%84%E7%BD%AE%E4%BF%A1%E5%8C%BA%E9%97%B4%E4%B8%BA%24(%5Coverline%7Bx_1%7D-%5Coverline%7Bx_2%7D)%20%5Cpm%20z_%7B%5Cfrac%7B%5Calpha%7D%7B2%7D%7D%5Csqrt%7B%5Cfrac%7B%5Csigma_1%5E2%7D%7Bn_1%7D%2B%5Cfrac%7B%5Csigma_2%5E2%7D%7Bn_2%7D%7D%24%0A%3E%24%5Csigma_1%5E2%2C%5Csigma_2%5E2%24%E5%B7%B2%E7%9F%A5%E6%97%B6%EF%BC%8C%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E5%9D%87%E5%80%BC%E4%B9%8B%E5%B7%AE%24%5Cmu_1-%5Cmu_2%24%E5%9C%A8%241-%5Calpha%24%E7%BD%AE%E4%BF%A1%E6%B0%B4%E5%B9%B3%E4%B8%8B%E7%9A%84%E7%BD%AE%E4%BF%A1%E5%8C%BA%E9%97%B4%E4%B8%BA%24(%5Coverline%7Bx_1%7D-%5Coverline%7Bx_2%7D)%20%5Cpm%20z_%7B%5Cfrac%7B%5Calpha%7D%7B2%7D%7D%20%5Csqrt%7B%5Cfrac%7Bs_1%5E2%7D%7Bn_1%7D%2B%5Cfrac%7Bs_2%5E2%7D%7Bn_2%7D%7D%24%0A%0A%3E%E7%8B%AC%E7%AB%8B%E5%B0%8F%E6%A0%B7%E6%9C%AC(%24%5Csigma_1%5E2%3D%5Csigma_2%5E2%24)%0A%3E1.%E5%81%87%E5%AE%9A%E6%9D%A1%E4%BB%B6%0A%3E%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E9%83%BD%E6%9C%8D%E4%BB%8E%E6%AD%A3%E6%80%81%E5%88%86%E5%B8%83%0A%3E%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E6%96%B9%E5%B7%AE%E6%9C%AA%E7%9F%A5%E4%BD%86%E6%98%AF%E7%9B%B8%E7%AD%89(%5Csigma_1%5E2%3D%5Csigma_2%5E2)%0A%3E%E4%B8%A4%E4%B8%AA%E7%8B%AC%E7%AB%8B%E7%9A%84%E5%B0%8F%E6%A0%B7%E6%9C%AC(%24%5Cn_1%3C30%24%E5%92%8C%24n_2%3C30%24)%0A%3E2.%E6%80%BB%E4%BD%93%E6%96%B9%E5%B7%AE%E7%9A%84%E5%90%88%E5%B9%B6%E4%BC%B0%E8%AE%A1%E9%87%8F%0A%3E%24s_p%5E2%3D%5Cfrac%7B(n_1-1)s_1%5E2%2B(n_2-1)s_2%5E2%7D%7Bn_1%2Bn_2-2%7D%24%0A%3E3.%E4%BC%B0%E8%AE%A1%E9%87%8F%24%5Coverline%7Bx_1%7D-%5Coverline%7Bx_2%7D%24%E7%9A%84%E6%8A%BD%E6%A0%B7%E6%A0%87%E5%87%86%E5%B7%AE%0A%3E%24%5Csqrt%7B%5Cfrac%7Bs_p%5E2%7D%7Bn_1%7D%2B%5Cfrac%7Bs_p%5E2%7D%7Bn_2%7D%7D%3Ds_p%5Csqrt%7B%5Cfrac%7B1%7D%7Bn_1%7D%2B%5Cfrac%7B1%7D%7Bn_2%7D%7D%24%0A%3E%E4%B8%A4%E4%B8%AA%E6%A0%B7%E6%9C%AC%E5%9D%87%E5%80%BC%E4%B9%8B%E5%B7%AE%E7%9A%84%E6%A0%87%E5%87%86%E5%8C%96%0A%3E%24t%3D%5Cfrac%7B(%5Coverline%7Bx_1%7D-%5Coverline%7Bx_2%7D)-(%5Cmu_1-%5Cmu_2)%7D%7Bs_p%5Csqrt%7B%5Cfrac%7B1%7D%7Bn_1%7D%2B%5Cfrac%7B1%7D%7Bn_2%7D%7D%7D~t(n_1%2Bn_2-2)%24%0A%3E%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E5%9D%87%E5%80%BC%E4%B9%8B%E5%B7%AE(%24%5Cmu_1-%5Cmu_2%24)%E5%9C%A8%241-%5Calpha%24%E5%9C%A8%E7%BD%AE%E4%BF%A1%E6%B0%B4%E5%B9%B3%E4%B8%8B%E7%9A%84%E7%BD%AE%E4%BF%A1%E5%8C%BA%E9%97%B4%E4%B8%BA%0A%3E%24(%5Coverline%7Bx_1%7D-%5Coverline%7Bx_2%7D)%20%5Cpm%20t_%7B%5Cfrac%7B%5Calpha%7D%7B2%7D%7D(n_1%2Bn_2-2)%5Csqrt%7Bs_p%5E2(%5Cfrac%7B1%7D%7Bn_1%7D%2B%5Cfrac%7B1%7D%7Bn_2%7D)%7D%24%0A%0A%3E%E7%8B%AC%E7%AB%8B%E5%B0%8F%E6%A0%B7%E6%9C%AC(%24%5Csigma_1%5E2%20%5Cneq%20%5Csigma_2%5E2%24)%0A%3E1.%E5%81%87%E5%AE%9A%E6%9D%A1%E4%BB%B6%0A%3E%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E9%83%BD%E6%9C%8D%E4%BB%8E%E6%AD%A3%E6%80%81%E5%88%86%E5%B8%83%0A%3E%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E6%96%B9%E5%B7%AE%E6%9C%AA%E7%9F%A5%E4%B8%94%E4%B8%8D%E7%9B%B8%E7%AD%89%EF%BC%8C%24%5Calpha_1%5E2%20%5Cneq%20%5Calpha_2%5E2%24%0A%3E%E4%B8%A4%E4%B8%AA%E7%8B%AC%E7%AB%8B%E7%9A%84%E5%B0%8F%E6%A0%B7%E6%9C%AC(%24n_1%3C30%2Cn_2%3C30%24)%0A%3E2.%E4%BD%BF%E7%94%A8%E7%BB%9F%E8%AE%A1%E9%87%8F%0A%3E%24t%3D%5Cfrac%7B(%5Coverline%7Bx_1%7D-%5Coverline%7Bx_2%7D)%7D%7B%20%5Csqrt%7B%5Cfrac%7Bs_1%5E2%7D%7Bn_1%7D%2B%5Cfrac%7Bs_2%5E2%7D%7Bn_2%7D%7D%7D~t(v)%24%0A%0A%3E%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E5%9D%87%E5%80%BC%E4%B9%8B%E5%B7%AE(%24%5Cmu_1-%5Cmu_2%24)%E5%9C%A8%241-%5Calpha%24%E7%BD%AE%E4%BF%A1%E6%B0%B4%E5%B9%B3%E4%B8%8B%E7%9A%84%E7%BD%AE%E4%BF%A1%E5%8C%BA%E9%97%B4%E4%B8%BA%0A%3E%24(%5Coverline%7Bx_1%7D-%5Coverline%7Bx_2%7D)%20%5Cpm%20t_%7B%5Cfrac%7B%5Calpha%7D%7B2%7D%7D(v)%5Csqrt%7B%5Cfrac%7Bs_1%5E2%7D%7Bn_1%7D%2B%5Cfrac%7Bs_2%5E2%7D%7Bn_2%7D%7D%24%0A%3E%E5%85%B6%E4%B8%ADv%E6%98%AF%E6%8C%87%E8%87%AA%E7%94%B1%E5%BA%A6%2C%24v%3D%5Cfrac%7B(%5Cfrac%7Bs_1%5E2%7D%7Bn1%7D%2B%5Cfrac%7Bs_2%5E2%7D%7Bn_2%7D)%7D%7B%5Cfrac%7B(%5Cfrac%7Bs_1%5E2%7D%7Bn_1%7D)%7D%7Bn_1-1%7D%2B%5Cfrac%7B(%5Cfrac%7Bs_2%5E2%7D%7Bn_1%7D)%7D%7Bn_2-1%7D%7D%24%0A%3E%E5%8C%B9%E9%85%8D%E5%A4%A7%E6%A0%B7%E6%9C%AC%0A%3E1.%E5%81%87%E5%AE%9A%E6%9D%A1%E4%BB%B6%0A%3E%E4%B8%A4%E4%B8%AA%E5%8C%B9%E9%85%8D%E7%9A%84%E5%A4%A7%E6%A0%B7%E6%9C%AC(%24n_1%20%5Cgeq%2030%24%E5%92%8C%24n_2%20%5Cgeq%2030%24)%0A%3E%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E5%90%84%E8%A7%82%E5%AF%9F%E5%80%BC%E7%9A%84%E9%85%8D%E5%AF%B9%E5%B7%AE%E6%9C%8D%E4%BB%8E%E6%AD%A3%E6%80%81%E5%88%86%E5%B8%83%0A%3E2.%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E5%9D%87%E5%80%BC%E4%B9%8B%E5%B7%AE(%24%5Cmu_d%3D%5Cmu_1-%5Cmu_2%24%E5%9C%A8%241-%5Calpha%24)%E7%BD%AE%E4%BF%A1%E6%B0%B4%E5%B9%B3%E4%B8%8B%E7%9A%84%E7%BD%AE%E4%BF%A1%E5%8C%BA%E9%97%B4%0A%3E%24%5Coverline%7Bd%7D%20%5Cpm%20z_%7B%5Cfrac%7B%5Calpha%7D2%7D%5Cfrac%7B%5Csigma_d%7D%7B%5Csqrt%7Bn%7D%7D%24%0A%3E%E5%8C%B9%E9%85%8D%E5%B0%8F%E6%A0%B7%E6%9C%AC%0A%3E1.%E5%81%87%E5%AE%9A%E6%9D%A1%E4%BB%B6%0A%3E%E4%B8%A4%E4%B8%AA%E5%8C%B9%E9%85%8D%E7%9A%84%E5%B0%8F%E6%A0%B7%E6%9C%AC(%24n_1%3C30%24%E5%92%8C%24n_2%3C30%24)%0A%3E%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E5%90%84%E8%A7%82%E5%AF%9F%E5%80%BC%E7%9A%84%E9%85%8D%E5%AF%B9%E5%B7%AE%E6%9C%8D%E4%BB%8E%E6%AD%A3%E6%80%81%E5%88%86%E5%B8%83%0A%3E%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E5%9D%87%E5%80%BC%E4%B9%8B%E5%B7%AE(%24%5Cmu_d%3D%5Cmu_1-%5Cmu_2%24)%E5%9C%A8%241-%5Calpha%24%E7%BD%AE%E4%BF%A1%E6%B0%B4%E5%B9%B3%E4%B8%8B%E7%9A%84%E7%BD%AE%E4%BF%A1%E5%8C%BA%E9%97%B4%E4%B8%BA%24%5Coverline%7Bd%7D%20%5Cpm%20t_%7B%5Cfrac%7B%5Calpha%7D%7B2%7D%7D(n-1)%5Cfrac%7Bs_d%7D%7B%5Csqrt%7Bn%7D%7D%24%0A%0A%0A%23%23%23%23%20%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E6%AF%94%E4%BE%8B%E4%B9%8B%E5%B7%AE%E7%9A%84%E5%8C%BA%E9%97%B4%E4%BC%B0%E8%AE%A1%0A%3E1.%E5%81%87%E5%AE%9A%E6%9D%A1%E4%BB%B6%0A%3E%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E6%9C%8D%E4%BB%8E%E4%BA%8C%E9%A1%B9%E5%88%86%E5%B8%83%0A%3E%E5%8F%AF%E4%BB%A5%E7%94%A8%E6%AD%A3%E6%80%81%E5%88%86%E5%B8%83%E6%9D%A5%E8%BF%91%E4%BC%BC%0A%3E%E4%B8%A4%E4%B8%AA%E6%A0%B7%E6%9C%AC%E6%98%AF%E7%8B%AC%E7%AB%8B%E7%9A%84%0A%3E2.%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E6%AF%94%E4%BE%8B%E4%B9%8B%E5%B7%AE%24%5Cpi_1-%5Cpi_2%24%E5%9C%A8%241-%5Calpha%24%E7%BD%AE%E4%BF%A1%E6%B0%B4%E5%B9%B3%E4%B8%8B%E7%9A%84%E7%BD%AE%E4%BF%A1%E5%8C%BA%E9%97%B4%E4%B8%BA%0A%3E%24(p_1-p_2)%20%5Cpm%20z_%7B%5Cfrac%7B%5Calpha%7D%7B2%7D%7D%5Csqrt%7B%5Cfrac%7Bp_1(1-p_1)%7D%7Bn_1%7D%2B%5Cfrac%7Bp_2(1-p_2)%7D%7Bn_2%7D%7D%24%0A%0A%0A%23%23%23%23%20%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E6%96%B9%E5%B7%AE%E6%AF%94%E7%9A%84%E5%8C%BA%E9%97%B4%E4%BC%B0%E8%AE%A1%0A%3E1.%E6%AF%94%E8%BE%83%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E7%9A%84%E6%96%B9%E5%B7%AE%E6%AF%94%0A%3E2.%E7%94%A8%E4%B8%A4%E4%B8%AA%E6%A0%B7%E6%9C%AC%E7%9A%84%E6%96%B9%E5%B7%AE%E6%AF%94%E6%9D%A5%E5%88%A4%E6%96%AD%0A%3E*%20%E5%A6%82%E6%9E%9C%24%5Cfrac%7BS_1%5E2%7D%7BS_2%5E2%7D%24%E6%8E%A5%E8%BF%91%E4%BA%8E1%EF%BC%8C%E8%AF%B4%E6%98%8E%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E6%96%B9%E5%B7%AE%E5%BE%88%E6%8E%A5%E8%BF%91%0A%3E*%20%E5%A6%82%E6%9E%9C%24%5Cfrac%7BS_1%5E2%7D%7BS_2%5E2%7D%24%E8%BF%9C%E7%A6%BB1%EF%BC%8C%E8%AF%B4%E6%98%8E%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E6%96%B9%E5%B7%AE%E4%B9%8B%E9%97%B4%E5%AD%98%E5%9C%A8%E5%B7%AE%E5%BC%82%0A%3E3.%E6%80%BB%E4%BD%93%E6%96%B9%E5%B7%AE%E6%AF%94%E5%9C%A8%241-%5Calpha%24%E7%BD%AE%E4%BF%A1%E6%B0%B4%E5%B9%B3%E4%B8%8B%E7%9A%84%E7%BD%AE%E4%BF%A1%E5%8C%BA%E9%97%B4%0A%3E%24%5Cfrac%7B%5Cfrac%7Bs_1%5E2%7D%7Bs_2%5E2%7D%7D%7BF_%7B%5Cfrac%7B%5Calpha%7D%7B2%7D%7D%7D%20%5Cleq%20%5Cfrac%7B%5Csigma_1%5E2%7D%7B%5Csigma_2%5E2%7D%20%5Cleq%20%5Cfrac%7B%5Cfrac%7Bs_1%5E2%7D%7Bs_2%5E2%7D%7D%7BF_%7B1-%5Cfrac%7B%5Calpha%7D%7B2%7D%7D%24%0A%0A%23%23%23%20%E6%A0%B7%E6%9C%AC%E5%AE%B9%E9%87%8F%E7%9A%84%E7%A1%AE%E5%AE%9A%0A%23%23%23%23%20%E4%BC%B0%E8%AE%A1%E6%80%BB%E4%BD%93%E5%9D%87%E5%80%BC%E6%97%B6%E6%A0%B7%E6%9C%AC%E5%AE%B9%E9%87%8F%E7%9A%84%E7%A1%AE%E5%AE%9A%0A%3E1.%E4%BC%B0%E8%AE%A1%E6%80%BB%E4%BD%93%E5%9D%87%E5%80%BC%E6%97%B6%E6%A0%B7%E6%9C%AC%E5%AE%B9%E9%87%8Fn%E4%B8%BA%0A%3E%24n%3D%5Cfrac%7Bz_%7B%5Cfrac%7B%5Calpha%7D%7B2%7D%7D%5E2%5Csigma%5E2%7D%7BE%5E2%7D%24%0A%3E2.%E6%A0%B7%E6%9C%AC%E5%AE%B9%E9%87%8Fn%E4%B8%8E%E6%80%BB%E4%BD%93%E6%96%B9%E5%B7%AE%24%5Csigma%5E2%24%2C%E8%BE%B9%E9%99%85%E8%AF%AF%E5%B7%AEE%E5%92%8C%E5%8F%AF%E9%9D%A0%E6%80%A7%E7%B3%BB%E6%95%B0Z%E6%88%96t%E4%B9%8B%E9%97%B4%E7%9A%84%E5%85%B3%E7%B3%BB%E4%B8%BA%0A%3E*%20%E4%B8%8E%E6%80%BB%E4%BD%93%E6%96%B9%E5%B7%AE%E6%88%90%E6%AD%A3%E6%AF%94%0A%3E*%20%E4%B8%8E%E8%BE%B9%E9%99%85%E8%AF%AF%E5%B7%AE%E6%88%90%E5%8F%8D%E6%AF%94%0A%3E*%20%E4%B8%8E%E5%8F%AF%E9%9D%A0%E6%80%A7%E7%B3%BB%E6%95%B0%E6%88%90%E6%AD%A3%E6%AF%94%0A%0A%0A%23%23%23%23%20%E4%BC%B0%E8%AE%A1%E6%80%BB%E4%BD%93%E6%AF%94%E4%BE%8B%E6%97%B6%E6%A0%B7%E6%9C%AC%E5%AE%B9%E9%87%8F%E7%9A%84%E7%A1%AE%E5%AE%9A%0A%3E1.%E6%A0%B9%E6%8D%AE%E6%AF%94%E4%BE%8B%E5%8C%BA%E9%97%B4%E4%BC%B0%E8%AE%A1%E5%85%AC%E5%BC%8F%E5%8F%AF%E5%BE%97%E6%A0%B7%E6%9C%AC%E5%AE%B9%E9%87%8F%0A%3E%24n%3D%5Cfrac%7B(z_%7Bfrac%7B%5Calpha%7D%7B2%7D%7D)%5E2%5C%20dot%20%5Cpi(1-%5Cpi)%7D%7BE%5E2%7D%24%0A%3E%E5%85%B6%E4%B8%AD%20%24E%3Dz_%7B%5Cfrac%7B%5Calpha%7D%7B2%7D%5Csqrt%7B%5Cfrac%7B%5Cpi(1-%5Cpi)%7D%7Bn%7D%7D%7D%24%0A%3E2.E%E7%9A%84%E5%8F%96%E5%80%BC%E4%B8%80%E8%88%AC%E5%B0%8F%E4%BA%8E0.1%0A%3E3.%24%5Cpi%24%E6%9C%AA%E7%9F%A5%E6%97%B6%EF%BC%8C%E5%8F%AF%E5%8F%96%E6%9C%80%E5%A4%A7%E5%80%BC0.5%0A%0A%0A%23%23%23%23%20%E4%BC%B0%E8%AE%A1%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E5%9D%87%E5%80%BC%E4%B9%8B%E5%B7%AE%E6%97%B6%E6%A0%B7%E6%9C%AC%E5%AE%B9%E9%87%8F%0A%3E1.%E8%AE%BE%24n_1%24%E5%92%8C%24n_2%24%E6%9D%A5%E8%87%AA%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E7%9A%84%E6%A0%B7%E6%9C%AC%EF%BC%8C%E5%B9%B6%E5%81%87%E5%AE%9A%24n_1%3Dn_2%24%0A%3E2.%E6%A0%B9%E6%8D%AE%E5%9D%87%E5%80%BC%E4%B9%8B%E5%B7%AE%E7%9A%84%E5%8C%BA%E9%97%B4%E4%BC%B0%E8%AE%A1%E5%85%AC%E5%BC%8F%E5%8F%AF%E5%BE%97%E4%B8%A4%E4%B8%AA%E6%A0%B7%E6%9C%AC%E7%9A%84%E5%AE%B9%E9%87%8Fn%E4%B8%BA%0A%3E%24n_1%3Dn_2%3Dn%3D%5Cfrac%7B(z_%7B%5Cfrac%7B%5Calpha%7D%7B2%7D%7D)(%5Csigma_1%5E2%2B%5Csigma_2%5E2)%7D%7BE%5E2%7D%24%0A%3E%E5%85%B6%E4%B8%AD%24E%3Dz_%7B%5Cfrac%7B%5Calpha%7D%7B2%7D%5Cfrac%7B%5Csigma_1%2B%5Csigma_2%7D%7B%5Csqrt%7Bn%7D%7D%7D%24%0A%0A%0A%23%23%23%23%20%E4%BC%B0%E8%AE%A1%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E6%AF%94%E4%BE%8B%E4%B9%8B%E5%B7%AE%E6%97%B6%E6%A0%B7%E6%9C%AC%E5%AE%B9%E9%87%8F%0A%3E1.%E8%AE%BE%24n_1%24%E5%92%8C%24n_2%24%E6%9D%A5%E8%87%AA%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E7%9A%84%E6%A0%B7%E6%9C%AC%EF%BC%8C%E5%B9%B6%E5%81%87%E5%AE%9A%24n_1%3Dn_2%24%0A%3E2.%E6%A0%B9%E6%8D%AE%E6%AF%94%E4%BE%8B%E4%B9%8B%E5%B7%AE%E7%9A%84%E5%8C%BA%E9%97%B4%E4%BC%B0%E8%AE%A1%E5%85%AC%E5%BC%8F%E5%8F%AF%E5%BE%97%E4%B8%A4%E4%B8%AA%E6%A0%B7%E6%9C%AC%E7%9A%84%E5%AE%B9%E9%87%8Fn%E4%B8%BA%0A%3E%24n_1%3Dn_2%3Dn%3D%5Cfrac%7B(z_%7Bfrac%7B%5Calpha%7D%7B2%7D%7D)%5E2%5B%5Cpi_1(1-%5Cpi_1)%2B%5Cpi_2(1-%5Cpi_2)%5D%7D%7BE%5E2%7D%24%0A%3E%E5%85%B6%E4%B8%AD%24E%3Dz_%7B%5Cfrac%7B%5Calpha%7D%7B2%7D%7D%5Cfrac%7B%5Cpi_1(1-%5Cpi_1)%2B%5Cpi_2(1-%5Cpi_2)%7D%7B%5Csqrt%7Bn%7D%7D%24

 

posted on 2019-06-12 15:49  pandaboy1123  阅读(2906)  评论(0编辑  收藏  举报

导航