Use the following values from Student’s t-distribution to establish a 95% confidence interval for the population mean given a sample size of 10, a sample mean of 6.25, and a sample standard deviation 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:
Calculate and interpret a confidence interval for a population mean, given a normal distribution with 1) a known population variance, 2) an unknown population variance, or 3) an unknown variance and a large sample size.
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 begin 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 we have:
