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Helen 🎈 · 2023年06月23日

为啥用Z?不是总体方差未知总T吗

NO.PZ2015120604000147

问题如下:

Here is a table discribing sample statistics from two bonds' rate of return which are both normally distributed over the past decades. If an investor is considering whether the mean of bond B is greater than 26%,

which of the following conclusion is least appropriate (significant level=5%) ?

选项:

A.

It is appropriate to use the Z-test.

B.

The mean of bond B is not significant greater than 26%.

C.

It is a one-tailed test.

解释:

B is correct.

It is appropraite to ues the one-tailed Z-test because the sample size of bond B is bigger than 30.

The null hypothesis is: H0: μ 26%

The test statistic:


α= 5% indicates the critical value is equal to ±1.65.

Because 1.91>1.65, therefore, we should reject the null hypothesis.

如题。。。。。。。。。。

1 个答案

星星_品职助教 · 2023年06月25日

同学你好,

本题问的是bond B,对应sample size=49.

当N>30时,根据中心极限定理,样本均值近似服从正态分布,故可以使用z分布来作为替代。

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