Identify the null hypothesis, alternative hypothesis, test statistic, p-value or critical value, and the conclusion about the null hypothesis. Use the P-value method.

Question: When a fair die is rolled many times, the outcomes of 1, 2, 3, 4, 5, and 6 are equally likely, so the mean of the outcomes should be 3.5. The author drilled holes into the die and loaded it by inserting lead weights, then rolled it 16 times to obtain a mean of 2.9375. Assume that the standard deviation of the outcome is 1.7078, which is the standard deviation for a fair die. Use a 0.05 significance level to test the claim that outcomes from the loaded die have a mean different from the value of 3.5 expected with a fair die. Is there anything about the sample data suggesting that the methods of this section should not be used?