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Emma0627 · 2023年08月05日

为什么不能当做independent populations判断?

  1. CFA I
  2. Quantitative

NO.PZ2022071202000084

问题如下：

Question
Using the following sample results drawn as 25 paired observations from their underlying distributions, test whether the mean returns of the two portfolios differ from each other at the 1% level of statistical significance. Assume the underlying distributions of returns for each portfolio are normal and that their population variances are not known.

t-statistic for 24 degrees of freedom and at the 1% level of statistical significance = 2.807

Null hypothesis (H0): Mean difference of returns = 0

Based on the paired comparisons test of the two portfolios, the most appropriate conclusion is that H0 should be:

选项：

A.rejected because the computed test statistic exceeds 2.807. B.accepted because the computed test statistic exceeds 2.807. C.accepted because the computed test statistic is less than 2.807.

解释：

Solution

A is correct.

In this case, the test statistic equals: (4.25-0)/(6.25/√25)= 3.40. Because 3.40 > 2.807, the null hypothesis that the mean difference is zero is rejected.

B is incorrect because a too large (or too small) test statistic leads to the rejection of the null hypothesis.

C is incorrect because the correctly computed test statistic exceeds the critical value of 2.807. A reasonable way to reach response C is to fail to divide the standard error by the square root of the sample size, erroneously using 4.25/6.25 = 0.68 as the test statistic.

我通过给出的两个标准差算t检验，表格第四行two independent populations和paired comparison有什么区别？

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1 个答案

星星_品职助教 · 2023年08月06日

同学你好，

paired comparison test的前提就是样本的抽取不独立（dependent samples），故该test的t统计量计算公式和independent samples的公式是截然不同的。

本题已经明确要求要“Based on the paired comparisons test”，所以只能用paired的公式，不能用其他公式。

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NO.PZ2022071202000084问题如下QuestionUsing the following sample results awn 25 paireobservations from their unrlying stributions, test whether the mereturns of the two portfolios ffer from eaother the 1% level of statisticsignificance. Assume the unrlying stributions of returns for eaportfolio are normanththeir population variances are not known.t-statistic for 24 grees of freem anthe 1% level of statisticsignifican= 2.807Null hypothesis (H0): Mefferenof returns = 0Baseon the pairecomparisons test of the two portfolios, the most appropriate conclusion is thH0 shoulbe:A.rejectebecause the computetest statistic excee 2.807.B.acceptebecause the computetest statistic excee 2.807.C.acceptebecause the computetest statistic is less th2.807. SolutionA is correct. In this case, the test statistic equals: (4.25-0)/(6.25/√25)= 3.40. Because 3.40 2.807, the null hypothesis ththe mefferenis zero is rejecteB is incorrebecause a too large (or too small) test statistic lea to the rejection of the null hypothesis.C is incorrebecause the correctly computetest statistic excee the criticvalue of 2.807. A reasonable wto rearesponse C is to fail to vi the stanrerror the square root of the sample size, erroneously using 4.25/6.25 = 0.68 the test statisti请问是哪个公式，有记忆，但是咋没找到，

2023-01-07 05:11 2 · 回答