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粗眉毛辣椒油 · 2024年02月06日

题目的意思

NO.PZ2020010304000049

问题如下:

Find the p-value for the following t-test statistics of the null hypothesis, H0:μ=μ0H_0: \mu = \mu_0.

a. Statistic: 1.45, Alternative: Two-sided

b. Statistic: 1.45, Alternative: One-sided upper

c. Statistic: 1.45, Alternative: One-sided lower

d. Statistic: -2.3, Alternative: One-sided upper

e. Statistic: 2.7, Alternative: Two-sided

选项:

解释:

a. In a two-sided test, the p-value is the area under the normal curve for values greater than 1.45 or less than -1.45. This is twice the area less than -1.45, or 2 * 0.074. = .148.

b. In a one-sided upper test, we need the area above 1.45. This is half the previous answer, or 0.074.

c. In a one-sided lower test, we need the area under the curve for values less than 1.45. This is just 1 - 0.074 = .926.

d. Here we need to probability under the normal curve for values above -2.3, which is 1 minus the area less than -2.3, or 1 - 0.01 = 0.99.

e. Because it is a two-sided alternative, we need that area for values larger than 2.7 or less than -2.7, which is twice the area less than -2.7. This value is 2 * .0034 = .0068.

题干是说statistic值为T分布,然后求P-value吗?

a.解析中,前半部分是说P-value指小于-1.45和大于1.45的面积,理解对吗?后半部分

“this is twice the area less than -1.45, or 2 * 0.074. = .148.”应该怎么理解呢?

这道题考点和解题思路是什么呢?谢谢。

1 个答案
已采纳答案

pzqa39 · 2024年02月07日

嗨,从没放弃的小努力你好:


这道题考察的是根据不同的t统计量,在t分布表里面查找对应的p value。

以第一小问为例,t值是1.45,要求是双尾检验,所以是求t值大于1.45的部分 + t值小于-1.45的部分。后半部分是在说,因为它查到的是小于-1.45的区域对应的p value是0.074,双尾的话还有右边大于1.45的部分,所以要乘2。


这道题不用太纠结了,考试不会这样去考的。拿t分布的表来举个例子:

我们考试当中一般是会给p=0.05或者0.025的t值(上面两列),再给自由度(左侧这列),让你去查t值判断是否拒绝H0。但是这道题是反过来了,给的是下面的t值,要求根据t值去查上面那两列p值,FRM考试的表格一般给不到这么全面的,而且自由度也没给。所以这道题不用太担心。


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