Question: Midland National Bank has a credit card division that sends out convenience checks attached to the company’s monthly statements. Customers can use these checks to make purchases or deposit them into their accounts. The average time it takes from the mail date to the time a customer uses one of these checks is 36 days. There is a standard deviation of 4 days. Now, the credit card division has started sending these checks out in their own individual envelopes. The manager believes that this has decreased the mean time from the mail date to the date of use of the checks. You perform a simple random sample of 50 customers and a 0.05 level of significance, and you find a sample mean of 34.37 days. Use a one-tailed hypothesis test, and complete the following steps.

a) Specify the population value of interest, and formulate the null and alternative hypotheses.

b) Determine the rejection region.

c) Compute the test statistic.

d) Set up the decision rule, and reach a decision.

e) Draw a conclusion.