Answer: [-3.466%, 11.466%]

The correct answer is A: [-3.466%, 11.466%]. The explanation for this is based on the principles of constructing a confidence interval for the mean when the population variance is unknown. Since the sample size is 30, the degrees of freedom for the t-distribution are 30 - 1 = 29. A t-reliability factor is used in place of the z-score because the population variance is not known. For a 95% confidence interval and a two-tailed test, the critical t-value from the t-table for 29 degrees of freedom at the 2.5th percentile is 2.045. The formula for the confidence interval is: \[ \text{CI} = \bar{x} \pm t_{\text{critical}} \times \frac{S_x}{\sqrt{n}} \] where: - \( \bar{x} \) is the sample mean (4% in this case), - \( t_{\text{critical}} \) is the critical t-value (2.045), - \( S_x \) is the sample standard deviation (20%), - \( n \) is the sample size (30). Plugging in the values, we get: \[ \text{CI} = 4\% \pm 2.045 \times \frac{20\%}{\sqrt{30}} \] Calculating the standard error of the mean (\( S_x / \sqrt{n} \)) gives us 3.651%. Multiplying this by the critical t-value and then adding and subtracting from the sample mean gives us the confidence interval: \[ \text{CI} = [4\% - 2.045 \times 3.651\%, 4\% + 2.045 \times 3.651\%] \] \[ \text{CI} = [-3.466\%, 11.466\%] \] This interval represents the range within which we can be 95% confident that the true mean monthly return of McCreary, Inc. lies.

Author: LeetQuiz Editorial Team