问一道题：NO.PZ2015120604000134

问题如下：

Ida Lee and his team collect a lot of statistical data about the car market .According to the data, they come to the conclusion that the mean price of SUV is more than $46,435 in his country. Then they randomly select 64 SUVs whose mean price is $46,760. Assume the standard deviation of the population is 1370. Ida Lee conducts a hypothesis test to check their conclusion. What is the value of the calculated test statistic?

选项：

4.2348

1.8978

1.5848

解释：

B is correct.

$z = \frac{46,760 - 46,435}{1370 / \sqrt{64}} = 1.8978$

这题的mean是sample的mean, standard deviation是population的也就是standard error，不是应该前后统一吗？那么题目不是也应该给出sample的standard deviation来进行计算吗？虽然这题我最后算对了，但是总是觉得很奇怪

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星星_品职助教 · 2020年04月02日

同学你好，

样本均值需要对应样本均值的标准差，即标准误，也就是你提的sample mean的standard deviation。

总体的标准差为σx，样本均值的标准差即标准误为Sx bar。把总体的标准差转化为样本均值的标准差的过程即为Sx bar=σx/√n。这是中心极限定理的应用。样本均值对应着样本均值的标准差，前后是统一的。

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