Ivana 🍭 · 2022年09月28日

# 这个公式:S/√n 得到的不是standard error 嘛，请问为什么不能用这个公式计算？

NO.PZ2015120604000125

The population is 6000 programmer which is supposed to be normally distributed. A sample with 100 size is drawn from the population. Based on z-statistic, 95% confidence interval of sample mean of annual salary is 32.5 (in thousands) dollars ranges from 22 (in thousands) dollars to 43 (in thousands) dollars .Calculate the standard error of mean annual salary:

A.

1.96.

B.

3.99.

C.

5.36.

C is correct.

At the 95% level of significance, the critical value is ${\text{z}}_{\alpha \text{/2}}=1.96$.

So the confidence interval is $32.5±1.96 \sigma {}_{\overline{x}}$,

From the equation t 32.5 + 1.96 σ${}_{\overline{x}}$ = 43 or 32.5 - 1.96σ ${}_{\overline{x}}$ = 22, we get ${\sigma }_{\overline{x}}=5.36.$=5.3571.

Ivana 🍭 · 2022年09月28日

###### 2 个答案

@Ivana 🍭

22到43是置信区间的范围，不是样本的数值。换而言之， 这个范围可以得到的是32.5 + 1.96 *standard error = 43 或 32.5 - 1.96 *standard error = 22

Ivana 🍭 · 2022年09月30日