A major department store chain is interested in estimating the mean amount its credit card customers spent on their first visit to the chain's new store in the mall. Fifteen credit card accounts were randomly sampled and analyzed with the following results: X = $50.50 and S = 20. Construct a 95% confidence interval for the mean amount its credit card customers spent on their first visit to the chain's new store in the mall assuming that the amount spent follows a normal distribution.
A) $50.50 ± $9.09
B) $50.50 ± $10.12
C) $50.50 ± $11.00
D) $50.50 ± $11.08

Question

Quizplus · Accepted Answer

The 95% confidence interval is calculated using the formula: X ± (t * (S/√n)), where t is the t-score for 95% confidence with 14 degrees of freedom (since n-1 = 15-1 = 14). The t-score is approximately 2.145. Thus, the interval is $50.50 ± (2.145 * (20/√15)) = $50.50 ± $11.08.

A Major Department Store Chain Is Interested in Estimating the Mean