A major department store chain is interested in estimating the average 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: $\overline{X} = \$50.50$ and s²= 400. Construct a 95% confidence interval for the average 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 ± $11.00 B) $50.50 ± $9.09 C) $50.50 ± $10.12 D) $50.50 ± $11.08

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Quizplus · Accepted Answer

The confidence interval is calculated using the formula: $\overline{X} \pm t_{\alpha/2} \times \frac{s}{\sqrt{n}}$. With n = 15, degrees of freedom = 14, and a 95% confidence level, the t-value is approximately 2.145. The standard deviation $s = \sqrt{400} = 20$. Thus, the margin of error is $2.145 \times \frac{20}{\sqrt{15}} \approx 11.08$.

A Major Department Store Chain Is Interested in Estimating the Average