In an application to estimate the mean number of miles that downtown employees commute to work roundtrip each day, the following information is given: n = 20 = 4.33 s = 3.50 Based on this information, the upper limit for a 95 percent confidence interval estimate for the true population mean is:
A) about 5.97 miles.
B) about 7.83 miles.
C) nearly 12.0 miles.
D) about 5.86 miles.

Question

Quizplus · Accepted Answer

The upper limit of a 95% confidence interval for the mean can be calculated using the formula: $\bar{x} + t_{\alpha/2} \times \frac{s}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $t_{\alpha/2}$ is the t-score for 95% confidence with $n-1$ degrees of freedom (here, 19), $s$ is the sample standard deviation, and $n$ is the sample size. Given $\bar{x} = 4.33$, $s = 3.50$, and $n = 20$, and knowing the t-score for 95% confidence and 19 degrees of freedom is approximately 2.093 (from t-distribution tables), the calculation is $4.33 + 2.093 \times \frac{3.50}{\sqrt{20}}$, which is approximately 5.97 miles.

In an Application to Estimate the Mean Number of Miles