A bank is testing a new method for getting delinquent customers to pay their past-due credit card bills. The standard way was to send a letter (costing about $0.45) asking the customer to pay. That worked 30% of the time. The bank wants to test a new method that involves sending a DVD to customers encouraging them to contact the bank and setup a payment plan. Developing and sending the video costs about $10 per customer.
The bank sets up the experiment to test the effectiveness of the DVD. They mail the DVD to a randomly selected sample of delinquent customers and keep track of how many actually do contact the bank to arrange payments.
Using the information from the experiment, the bank statistician calculated the 90% confidence interval for proportion of delinquent customers who make payments. The interval is:
(0.29, 0.45)
1. Since the old send-a-letter method worked 30% of the time, would this confidence interval lead the bank to decide that this new strategy is effective?
A) Since the interval includes 30%, the bank can assume the new strategy which utilizes the DVD is extremely effective.
B) Since the interval extends above and below 30%, the bank can assume the new strategy which utilizes the DVD is extremely effective.
C) Since the interval extends above and below 30%, the bank cannot assume the new strategy which utilizes the DVD is extremely effective.
D) The confidence interval is too wide for any conclusions.
2. Given the confidence interval calculated by the bank statistician, what would you recommend to the bank president? Should they move forward with the DVD strategy or scrap it?
A) The results are very clear; the DVD is very effective and the bank should switch immediately.
B) Since the confidence interval is so wide, the DVD strategy is clearly better.
C) Since the confidence interval extends below 30%, we are not convinced that the DVD is effective. It would be helpful to conduct the experiment again with a larger sample size.
D) Since the confidence interval extends below 30%, we are not convinced that the DVD is effective. It would be helpful to conduct the experiment again with a smaller sample size.
E) The confidence interval clearly shows that the DVD is not effective. The bank should scrap this idea.
3. The bank president thinks that the confidence interval is too wide. Which of the following would result in a narrower confidence interval?
I. Increase the confidence level
II. Decrease the confidence level
III. Increase the sample size
IV. Decrease the sample size
A) I only
B) II only
C) III only
D) IV only
E) I and III
F) II and III
G) II and IV
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