A major department store chain is interested in estimating the average amount its credit card customers spent. Fifteen credit card accounts were randomly sampled and analyzed with the following results: = $50.50 and = 400. Which of the following is a 95% confidence interval for the average amount the credit card customers spent?
A) $50.50$9.09
B) $50.50$10.12
C) $50.50$11.00
D) $50.50$11.08

Question

A major department store chain is interested in estimating the average amount its credit card customers spent. Fifteen credit card accounts were randomly sampled and analyzed with the following results:  = $50.50 and  = 400. Which of the following is a 95% confidence interval for the average amount the credit card customers spent?
A) $50.50$9.09 
B) $50.50$10.12 
C) $50.50$11.00 
D) $50.50$11.08

Quizplus · Accepted Answer

The sample mean is $50.50 and the sample standard deviation is $400. To calculate the confidence interval, we will use the t-distribution with 14 degrees of freedom (since n-1=14). Using a t-table or calculator, we find that the t-value for a 95% confidence interval with 14 degrees of freedom is approximately 2.145.

The margin of error is: 
$E = t*\frac{s}{\sqrt{n}} = 2.145*\frac{400}{\sqrt{15}} \approx 111.10$

Therefore, the 95% confidence interval is: 
$50.50 \pm 111.10$

Which simplifies to: 
$(39.40, 61.60)$

Thus, choice D is correct as it is the only option that contains 50.50 and a range of 11.08 or more.

A Major Department Store Chain Is Interested in Estimating the Average