A carpet company advertises that it will deliver your carpet within 15 days of purchase. A sample of 49 past customers is taken. The average delivery time in the sample was 16.2 days. The standard deviation of the population () is known to be 5.6 days. (show full calculation)

1. State the null and alternative hypotheses for a test to determine if their advertisement is legitimate.
2. Using the critical value approach, test the hypotheses. Let = .05.
3. Using the p-value approach, test the hypotheses at the 5% level of significance.