In this activity, we will test claims that the mean amount transferred for any single purchase is $0.50 and that the mean amount that Bank of America matches for a customer during the first 90 days of enrollment is at least $25.

1. Based on the assumption that all transfer amounts between $0.00 and $0.99 seem to be equally likely to occur, one may conclude that the mean of the amounts transferred is about $0.50. Explain how someone who doesn’t believe this conclusion would use a test of hypothesis to argue that the conclusion is false.

2. Suppose that your original data set Amounts Transferred from Activity 1.1 represents a random sample of amounts transferred for all Bank of America customers’ purchases.

Does your sample meet the requirements for performing either a large-sample or a small-sample test of hypothesis about the population mean? Explain. If your data meet the criteria for one of the tests, perform that test at α = .05.

3. Use the pooled data set of Amounts Transferred from Activity 4.2 to represent a random sample of amounts transferred for all Bank of America customers’ purchases.

Explain how the conditions for the large-sample test of hypothesis about a population mean are met. Then perform the test at α = .05. Do your results suggest that the mean may be something other than $0.50? Explain.

4. A friend suggests to you that the mean amount the bank matches for a customer during the first 90 days is at least $25. Explain how you could use a test of hypothesis to argue that your friend is wrong.

5. Suppose that your data set Bank Matching from Activity 1.1 represents a random sample of all Bank of America customers’ bank matching. Perform an appropriate test of hypothesis at α = .05 against your friend’s claim. Assume that the underlying distribution is normal, if necessary. Does the test provide evidence that your friend’s claim is false?

Keep the results from this activity for use in other activities.