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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

问题如下:

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:

选项:

A.

1.96.

B.

3.99.

C.

5.36.

解释:

C is correct.

At the 95% level of significance, the critical value is z α/2 =1.96 .

So the confidence interval is 32.5±1.96 σ x ¯ ,

From the equation t 32.5 + 1.96 σ x ¯ = 43 or 32.5 - 1.96 σ x ¯ = 22, we get σ x ¯ =5.36.=5.3571.


根据题干的sample mean=32.5,基于z-statistics的95%的置信区间(得到关键值±1.96),和置信区间的公式,可以得到 32.5 + 1.96 σ = 43 或 32.5 - 1.96 σ = 22。

得到 σ=5.3571


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?

Ivana 🍭 · 2022年09月28日

题目说范围是22到43,那将这些数输入计算器可以得到S 呀,请问为什么用上面这个公式计算不对?

2 个答案

星星_品职助教 · 2022年09月30日

@Ivana 🍭

追问已在单独的提问中回复,同样的问题提问一次即可。

星星_品职助教 · 2022年09月29日

同学你好,

本题并没有给出s,所以无法直接使用s除以根号n。

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

题目说范围是22到43,那将这些数输入计算器可以得到S 呀,请问为什么用上面这个公式计算不对? 22到43算出的平均数也刚好是题目中给的平均数,而且请问怎么判断23-43是置信区间?

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NO.PZ2015120604000125问题如下 The population is 6000 programmer whiis supposeto normally stribute A sample with 100 size is awn from the population. Baseon z-statisti95% confinintervof sample meof annusalary is 32.5 (in thousan) llars ranges from 22 (in thousan) llars to 43 (in thousan) llars .Calculate the stanrerror of meannusalary: A.1.96.B.3.99.C.5.36. C is correct.the 95% level of significance, the criticvalue is ±1.96.So the confinintervis 32.5±1.96 σ x ¯ , From the equation t 32.5 + 1.96 stanrerror = 43 or 32.5 - 1.96 stanrerror x ¯ = 22, we get σ x ¯ =5.36.=5.3571. 根据题干的sample mean=32.5,基于z-statistics的95%的置信区间(得到关键值±1.96),和置信区间的公式,可以得到 32.5 + 1.96 stanrerror = 43 或 32.5 - 1.96 stanrerror = 22。得到 stanrerror=5.3571 我可能公式有点搞混了,请问置信区间的计算什么时候使用 平均值+z×标准差,什么时候使用平均值+z×标准误

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