Dang.D · 2022年10月01日

# 怎么判断他是双尾的呢？

NO.PZ2017092702000113

For a sample size of 37, with a mean of 116.23 and a variance of 245.55, the width of a 90% confidence interval using the appropriate t-distribution is closest to:

A.

8.5480.

B.

8.6970

C.

8.8456.

B is correct.

The confidence interval is calculated using the following equation:$\overline X\pm t_{\alpha/2}\frac s{\sqrt n}$

Sample standard deviation (s) = $\sqrt{245.55}$ = 15.670.

For a sample size of 37, degrees of freedom equal 36, so t0.05 = 1.688.

The confidence interval is calculated as：

Therefore, the interval spans 120.5785 to 111.8815, meaning its width is equal to approximately 8.6970. (This interval can be alternatively calculated as 4.3485 × 2).

$\sqrt{245.55}$ = 15.670.