Question

3) A credit card company wants to find out how much, on average, was charged by its card holders last month. The company took a random sample of 100 card holders. An analyst reports that in this study, the average amount charged by card holders in the sample was $1,500 per month. She also reports that based on the information in this study, a 95% confidence interval for the average amount charged by card holders was $1,300 to $1,700 per month a) Provide an appropriate interpretation of this confidence interval estimate. (one sentence only) b) The company’s marketing department has suggested using the following statements in a press release. Classify each statement as misleading or wrong. Carefully explain why each statement is either misleading, or wrong: one sentence per statement. i) We are 95% confident that a randomly selected card holder will charge $1,300 - $1,700 per month. ii) With 95% confidence, the margin of error [for the CI estimate for the average amount charged by card holders] is $400 per month. iii) We think that 95% of the time the true average amount charged is $1,500 per month.

Answer 1

Here the monthly amount charged by card holders = $ 1500 per month

95% confidence interval = ($ 1300 - $ 1700 per month)

(a) Here the confidence interval means that if we take samples of size 100 repeatedly, there is approximately 95% confidence intervals will have average amount charged by card holders in between $ 1300 and $ 1500

(b) Here in this context, the confidence means the chance or probability of that thing happening so here it is 95% chance that the average credit card amount is in between $ 1300 to $ 1700

(c) (i) Wrong statement as the confidence interval is not applicable for a random card holder.

(ii) Here margin of error doesn't have a confidence level. so this is the not way to represent without giving average amount.

(iii) Average amount charged is not fixed and it will vary that's why we are calculating confidence interval.