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:
B is correct.
The confidence interval is calculated using the following equation:
Sample standard deviation (s) = = 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).
当样本=37，自由度=36，那么 t0.05 = 1.688.
因此，置信区间为：111.8815 - 120.5785，这意味着其宽度大约等于 8.6970。 （这个区间也可以计算为 4.3485 × 2）。