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.Fifteen credit card accounts were randomly sampled and analysed with the following results: $\bar { X }$ = $50.50 and S = 20.
-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 ± $10.12
C) $50.50 ± $9.09
D) $50.50 ± $11.08

Question

Quizplus · Accepted Answer

To construct a 95% confidence interval for the average amount spent, we use the formula: $\bar{X} \pm t_{\alpha/2} \cdot \frac{S}{\sqrt{n}}$, 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 $\bar{X} = 50.50$, $S = 20$, and $n = 15$, and knowing that the t-score for a 95% confidence interval with 14 degrees of freedom is approximately 2.145, we calculate the margin of error as $2.145 \cdot \frac{20}{\sqrt{15}} \approx 11.08$. Therefore, the 95% confidence interval is $50.50 ± $11.08.

A Major Department Store Chain Is Interested in Estimating the Average