《第七章 参数估计(4-).ppt

§4 区间估计 σ2 的 1-α置信区间为： σ 的 1-α置信区间为： Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. (续例1) 求总体标准差s的95%置信区间. 解: s的置信度为1??的置信区间为 这里 s的置信度为95%的置信区间为 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 二. 两个总体 的情况 两个总体均值差 的置信区间 样本： Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 的置信区间为： Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 由对称性： 解得置信区间为： Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 例2 为提高某一化学生产过程的得率，试图采用一种新的催化剂。为慎重起见，在试验工厂先进行试验。设采用原来的催化剂进行了n1=8次试验，得到得率的平均值 =91.73。样本方差s12=3.89 ; 又采用新的催化剂进行了n2=8次试验，得到得率的平均值 =93.75，样本方差s22=4.02 。假设两总体都可认为服从正态分布，且方差相等，两样本独立。试求两总体均值差?1-?2的置信水平为 0.95 的置信区间。 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 解： 置信区间为： 现在 故所求的置信区间为： 即 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 2. 两个总体方差比 的置信区间 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. * 前面，我们讨论了参数点估计。它是用样本算得的一个值去估计未知参数。但是，点估计值仅仅是未知参数的一个近似值，它没有反映出这个近似值的误差范围，使用起来把握不大。区间估计正好弥补了点估计的这个缺陷 。 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.