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猫咚 · 2019年11月28日

问一道题:NO.PZ2017092702000114

问题如下:

For a sample size of 65 with a mean of 31 taken from a normally distributed population with a variance of 529, a 99% confidence interval for the population mean will have a lower limit closest to:

选项:

A.

23.64.

B.

25.41.

C.

30.09.

解释:

A is correct.

To solve, use the structure of Confidence interval = Point estimate ± Reliability factor × Standard error, which, for a normally distributed population with known variance, is represented by the following formula:X±zα/2σn\overline X\pm z_{\alpha/2}\frac\sigma{\sqrt n}

For a 99% confidence interval, use z0.005 = 2.58. Also, σ = 529\sqrt{529} = 23. Therefore, the lower limit = .31  2.58 2365= 23.639831\text{ }-\text{ }2.58\text{ }\frac{23}{\sqrt{65}}=\text{ }23.6398

请问,为什么不用自由度64,还有单尾0.005查表t分布,而是直接用z分布的呢?是因为题目里面说了正态分布吗?

2 个答案
已采纳答案

星星_品职助教 · 2019年11月28日

同学你好,

如果这道题用t分布就是按照你说的那种方式查表。

不过这道题并不是因为总体是正态所以才用的Z。用Z的原因是总体方差已知,所以要用Z分布,就不涉及到自由度和尾部面积了。加油

bodane · 2019年11月28日

总体方差已知用z分布 总体方差未知t分布 当n大于30可以用正态分布  假设检验才会考虑单尾双尾

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NO.PZ2017092702000114 问题如下 For a sample size of 65 with a meof 31 taken from a normally stributepopulation with a varianof 529, a 99% confinintervfor the population mewill have a lower limit closest to: A.23.64. B.25.41. C.30.09. A is correct.To solve, use the structure of Confininterv= Point estimate ± Reliability factor × Stanrerror, which, for a normally stributepopulation with known variance, is representethe following formula:X‾±zα/2σn\overline X\pm z_{\alpha/2}\frac\sigma{\sqrt n}X±zα/2​n​σ​ For a 99% confininterval, use z0.005 = 2.58. Also, σ = 529\sqrt{529}529​ = 23. Therefore, the lower limit =31−2.58×2365=23.639831-2.58\times\frac{23}{\sqrt{65}}=23.639831−2.58×65​23​=23.6398 我们需要用到【置信区间结构】的计算公式解决本题the structure of Confininterv= Point estimate ± Reliability factor × Stanrerror即X‾±zα/2σn\overline X\pm z_{\alpha/2}\frac\sigma{\sqrt n}X±zα/2​n​σ​当置信区间=99%的时候,Z0.005=2.58,且 σ = 529\sqrt{529}529​ = 23. 所以,下限为 =31−2.58∗2365=23.6398=31-2.58*\frac{23}{\sqrt{65}}=23.6398=31−2.58∗65​23​=23.6398 老师,这种题型的计算思考步骤是什么呢,总是容易搞混,看题找不到方向?谢谢老师

2023-06-06 23:49 1 · 回答

NO.PZ2017092702000114 问题如下 For a sample size of 65 with a meof 31 taken from a normally stributepopulation with a varianof 529, a 99% confinintervfor the population mewill have a lower limit closest to: A.23.64. B.25.41. C.30.09. A is correct.To solve, use the structure of Confininterv= Point estimate ± Reliability factor × Stanrerror, which, for a normally stributepopulation with known variance, is representethe following formula:X‾±zα/2σn\overline X\pm z_{\alpha/2}\frac\sigma{\sqrt n}X±zα/2​n​σ​ For a 99% confininterval, use z0.005 = 2.58. Also, σ = 529\sqrt{529}529​ = 23. Therefore, the lower limit =31−2.58×2365=23.639831-2.58\times\frac{23}{\sqrt{65}}=23.639831−2.58×65​23​=23.6398 我们需要用到【置信区间结构】的计算公式解决本题the structure of Confininterv= Point estimate ± Reliability factor × Stanrerror即X‾±zα/2σn\overline X\pm z_{\alpha/2}\frac\sigma{\sqrt n}X±zα/2​n​σ​当置信区间=99%的时候,Z0.005=2.58,且 σ = 529\sqrt{529}529​ = 23. 所以,下限为 =31−2.58∗2365=23.6398=31-2.58*\frac{23}{\sqrt{65}}=23.6398=31−2.58∗65​23​=23.6398 请问为什么 No.PZ2017092702000113 (选择题),这道题的置信区间计算需要使用“分母根号下n-1”,即需要用自由度求解,但是这道题不需要呢?请问老师区别在哪里?谢谢老师

2023-04-12 16:32 1 · 回答

NO.PZ2017092702000114 问题如下 For a sample size of 65 with a meof 31 taken from a normally stributepopulation with a varianof 529, a 99% confinintervfor the population mewill have a lower limit closest to: A.23.64. B.25.41. C.30.09. A is correct.To solve, use the structure of Confininterv= Point estimate ± Reliability factor × Stanrerror, which, for a normally stributepopulation with known variance, is representethe following formula:X‾±zα/2σn\overline X\pm z_{\alpha/2}\frac\sigma{\sqrt n}X±zα/2​n​σ​ For a 99% confininterval, use z0.005 = 2.58. Also, σ = 529\sqrt{529}529​ = 23. Therefore, the lower limit =31−2.58×2365=23.639831-2.58\times\frac{23}{\sqrt{65}}=23.639831−2.58×65​23​=23.6398 我们需要用到【置信区间结构】的计算公式解决本题the structure of Confininterv= Point estimate ± Reliability factor × Stanrerror即X‾±zα/2σn\overline X\pm z_{\alpha/2}\frac\sigma{\sqrt n}X±zα/2​n​σ​当置信区间=99%的时候,Z0.005=2.58,且 σ = 529\sqrt{529}529​ = 23. 所以,下限为 =31−2.58∗2365=23.6398=31-2.58*\frac{23}{\sqrt{65}}=23.6398=31−2.58∗65​23​=23.6398 请问老师,我有两个问题,第一个是如果题干没有告诉我应该用到什么分布的话,我怎么判断是应该用z分布还是t分布呢?第二个问题是,我现在很混乱z分布和t分布的计算有什么区别呢》唯一的区别就是t分布的计算是自由度-1是吗,z分布就直接用sample zise的数量?

2022-12-13 06:49 1 · 回答

NO.PZ2017092702000114问题如下 For a sample size of 65 with a meof 31 taken from a normally stributepopulation with a varianof 529, a 99% confinintervfor the population mewill have a lower limit closest to:A.23.64. B.25.41. C.30.09. A is correct.To solve, use the structure of Confininterv= Point estimate ± Reliability factor × Stanrerror, which, for a normally stributepopulation with known variance, is representethe following formula:X‾±zα/2σn\overline X\pm z_{\alpha/2}\frac\sigma{\sqrt n}X±zα/2​n​σ​ For a 99% confininterval, use z0.005 = 2.58. Also, σ = 529\sqrt{529}529​ = 23. Therefore, the lower limit =31−2.58×2365=23.639831-2.58\times\frac{23}{\sqrt{65}}=23.639831−2.58×65​23​=23.6398 我们需要用到【置信区间结构】的计算公式解决本题the structure of Confininterv= Point estimate ± Reliability factor × Stanrerror即X‾±zα/2σn\overline X\pm z_{\alpha/2}\frac\sigma{\sqrt n}X±zα/2​n​σ​当置信区间=99%的时候,Z0.005=2.58,且 σ = 529\sqrt{529}529​ = 23. 所以,下限为 =31−2.58∗2365=23.6398=31-2.58*\frac{23}{\sqrt{65}}=23.6398=31−2.58∗65​23​=23.6398 ​为什么样本标准差不是除以根号64呢?

2022-11-06 16:45 1 · 回答

NO.PZ2017092702000114问题如下 For a sample size of 65 with a meof 31 taken from a normally stributepopulation with a varianof 529, a 99% confinintervfor the population mewill have a lower limit closest to:A.23.64. B.25.41. C.30.09. A is correct.To solve, use the structure of Confininterv= Point estimate ± Reliability factor × Stanrerror, which, for a normally stributepopulation with known variance, is representethe following formula:X‾±zα/2σn\overline X\pm z_{\alpha/2}\frac\sigma{\sqrt n}X±zα/2​n​σ​ For a 99% confininterval, use z0.005 = 2.58. Also, σ = 529\sqrt{529}529​ = 23. Therefore, the lower limit =31−2.58×2365=23.639831-2.58\times\frac{23}{\sqrt{65}}=23.639831−2.58×65​23​=23.6398 我们需要用到【置信区间结构】的计算公式解决本题the structure of Confininterv= Point estimate ± Reliability factor × Stanrerror即X‾±zα/2σn\overline X\pm z_{\alpha/2}\frac\sigma{\sqrt n}X±zα/2​n​σ​当置信区间=99%的时候,Z0.005=2.58,且 σ = 529\sqrt{529}529​ = 23. 所以,下限为 =31−2.58∗2365=23.6398=31-2.58*\frac{23}{\sqrt{65}}=23.6398=31−2.58∗65​23​=23.6398 ​为什么这个n用的65,但是上一题t分布里面n用的n37,查表用的 36呢?

2022-07-07 15:19 1 · 回答