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18816562889 · 2022年06月14日

为什么已知方差的情况下还用T检验

NO.PZ2015120604000145

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 A is equal to 22%,

which of the following conclusion is least appropriate (significant level=1%) ?

选项:

A.

The null hypothesis can be rejected.

B.

It is appropriate to use a two-tailed t-test.

C.

The test statistic value is 1.333.

解释:

A is correct.

The null hypothesis: H0: μ=22%.

Because the sample size is 25, which is less than 30, so it is appropriate to use the two-tailed t-test.

t=Xμ0sn=(0.260.22)0.1525=1.33t=\frac{(X-\mu_0)}{\frac s{\sqrt n}}={\textstyle\frac{(0.26-0.22)}{\textstyle\frac{0.15}{\sqrt{25}}}}=1.33

t at α= 0.01= ±2.797;

Because -2.797 <1.333<+2.797, therefore, H0 cannot be rejected.

不是已知方差用的是Z吗

1 个答案

星星_品职助教 · 2022年06月14日

同学你好,

总体方差已知用z,总体方差未知用t,本题总体方差是未知的,给出的只是样本的standard deviation,所以应该用t检验

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