One Sample Hypothesis Test: A credit card company wondered whether giving frequent flyer miles for every purchase would increase card usage, which has a current mean of $2500 per year. They gave free miles to 51 credit card customers and found their mean credit card purchases to be $2542 per year. Assume the population standard deviation is $112. Given this data perform a hypothesis test, at = 0.01, to see if the customers increased their card usage.

1. Identify the null hypothesis, Ho, and the alternative hypothesis, Ha.
2. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.
3. Find the critical value(s) and identify the rejection region(s).
4. Find the appropriate standardized test statistic. If convenient, use technology.
5. Decide whether to reject or fail to reject the null hypothesis.
6. Interpret the decision in the context of the original claim.