单选题

Use the following values from a student's t-distribution to establish a 95% confidence interval for the opulation mean given a sample size of 10, a sample mean of 6.25, and a sample standard eviation of 12. Assume that the population from which the sample is drawn is normally distributed and the population variance is not known.

Degrees of Freedom	p=0.10	p=0.05	p=0.025	p = 0.01
9	1.383	1.833	2.262	2.821
10	1.372	1.812	2.228	2.764
11	1.363	1.796	2.201	2.718

The 95% confidence interval is closest to a:

A、 lower bound of -0.71 and an upper bound of 13.21.
B、 lower bound of -2.20 and an upper bound of 14.70.
C、 lower bound of -2.33 and an upper bound of 14.83.

【正确答案】 C

【答案解析】

With a sample size of 10, there are 9 degrees of freedom. The confidence interval concept is based on a two-tailed approach. For a 95% confidence interval,2.5% of the distribution will be in each tail. Thus, the correct t-statistic to use is 2.262. The confidence interval is calculated as:

where is the sample mean, s is the sample standard deviation, and n is the sample size. In this case: