题目中没有提到critical value是双尾还是单位的value。是否默认为单尾得到value？

问题如下：

For a sample of the past 30 monthly stock returns for McCreary, Inc., the mean return is 4% and the sample standard deviation is 20%. The population variance is unknown but the standard error of the sample mean is estimated to be:

The related t-table values are shown below (ti,j denotes the (100-j) th percentile of t-distribution value with i degrees of freedom):

What is the 95% confidence interval for the mean monthly return?

选项：

A.

[-3.466%, 11.466%]

B.

[-3.453%, 11.453%]

C.

[-2.201%, 10.201%]

D.

[-2.194%, 10.194%]

解释：

中文解析：

自由度=30-1=29

t检验是双尾检验，单尾是2.5%

查表得检测值=2.045

变量的变化范围=均值+/- 检测值*σ

[4% − 2.045(3.651%), 4% + 2.045(3.651%)] = [−3.466%, 11.466%]

选A

Here the t-reliability factor is used since the population variance is unknown. Since there are 30 observations, the degrees of freedom are 30 - 1 = 29. The t-test is a two-tailed test. So, the correct critical t-value is t29,2.5 = 2.045, thus the 95% confidence interval for the mean return is:

[4% − 2.045(3.651%), 4% + 2.045(3.651%)] = [−3.466%, 11.466%]