Final answer:
To estimate the 95% confidence interval for the difference between the average purchases of customers using the store's credit card and a major credit card, we use the given population standard deviations, sample sizes, and sample means along with the Z-value for a 95% confidence level.
Step-by-step explanation:
The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store's credit card versus those using a national major credit card. To find a 95% confidence interval estimate for the difference between the average purchases, we utilize the fact that both population standard deviations are known. The formula for the confidence interval is: Zα/2 * √((σx2/nx) + (σy2/ny)),
where Zα/2 is the Z-value from the standard normal distribution corresponding to the desired confidence level (1.96 for 95%), σ2 represents the population variance, and n is the sample size. Plugging in the values given for the store's and the major credit card, we calculate the margin of error and add it to and subtract it from the difference between the sample means to find the confidence interval.