1. A company advertises that they will deliver any Internet orders within 4 days. A sample of 36 past customers shows an average delivery time of 6.2 days with a standard deviation of 4.8 days. State the null and alternative hypotheses and test the hypothesis at the 99% confidence level using the P-value to determine if the company's advertisement is truthful.
2. A municipal water board claims the average monthly water bill of its customers is $48. A random sample of 25 customers finds a mean bill of $52 and a standard deviation of $6. Should the board's claims be trusted? Use a .02 level of significance and the confidence interval approach to justify your answer.