The Dean of the Business School wants to estimate the mean number of hours worked per week by students. A sample of only 12 students showed a mean of 24 hours with a standard deviation of 4 hours. Find the 95 percent confidence interval for the population mean.
A) 21.46 and 26.54
B) 21.17 and 26.45
C) 22.88 and 25.12
D) 21.07 and 26.07
E) 21.93 and 26.07

Question

Quizplus · Accepted Answer

The 95% confidence interval for the population mean can be calculated using the formula: $\bar{x} \pm t_{\alpha/2} \times \frac{s}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $s$ is the sample standard deviation, $n$ is the sample size, and $t_{\alpha/2}$ is the t-score for a 95% confidence level with $n-1$ degrees of freedom. Given $\bar{x} = 24$, $s = 4$, and $n = 12$, and knowing that the t-score for 95% confidence with 11 degrees of freedom is approximately 2.201, the interval is calculated as $24 \pm 2.201 \times \frac{4}{\sqrt{12}}$, resulting in approximately 21.46 and 26.54.

The Dean of the Business School Wants to Estimate the Mean