A study reports that 22 people experienced relief with an average time of 13 minutes and a standard deviation of 4 minutes. To construct a 95% confidence interval for the population mean relief time, which method is appropriate?

A study reports that 22 people experienced relief with an average time of 13 minutes and a standard deviation of 4 minutes. To construct a 95% confidence interval for the population mean relief time, which method is appropriate?

• A. 1-sample t-interval with 21 degrees of freedom
• B. 1-sample z-interval for the mean
• C. Two-sample t-interval
• D. Chi-square interval for a mean

Answer: (A)

Using a one-sample t-interval is appropriate when estimating a population mean from a single sample and the population standard deviation is unknown. In this case, you estimate the standard deviation with the sample standard deviation and use the t-distribution with n−1 degrees of freedom to account for extra uncertainty. With n = 22, you have 21 degrees of freedom. For a 95% interval, the critical value is the t value at 0.025 in each tail with 21 df, which is about 2.08. The standard error is s/√n = 4/√22 ≈ 0.854, so the margin of error is 2.08 × 0.854 ≈ 1.78. The confidence interval for the population mean relief time is about 13 ± 1.78, i.e., roughly (11.2, 14.8). The z-interval would be used only if the population standard deviation were known. The two-sample t-interval applies to comparing two means from independent samples. The chi-square interval is for estimating a population variance (or standard deviation), not the mean.

Using a one-sample t-interval is appropriate when estimating a population mean from a single sample and the population standard deviation is unknown. In this case, you estimate the standard deviation with the sample standard deviation and use the t-distribution with n−1 degrees of freedom to account for extra uncertainty. With n = 22, you have 21 degrees of freedom. For a 95% interval, the critical value is the t value at 0.025 in each tail with 21 df, which is about 2.08. The standard error is s/√n = 4/√22 ≈ 0.854, so the margin of error is 2.08 × 0.854 ≈ 1.78. The confidence interval for the population mean relief time is about 13 ± 1.78, i.e., roughly (11.2, 14.8).

The z-interval would be used only if the population standard deviation were known. The two-sample t-interval applies to comparing two means from independent samples. The chi-square interval is for estimating a population variance (or standard deviation), not the mean.