Question: According to the Bureau of Labor Statistics, the average weekly earnings of a production worker in 1997 were $424.20. You are interested to know if wages, on average, have gone up. To test this, you sample 64 production workers, and determine that their average salary is $432.69, with a sample standard deviation of $33.90. Use a 0.05 level of significance.

a. State the null and alternative hypothesis that best tests the hypothesis of interest. Be sure the alternative hypothesis reflects the question of interest.

b. Carry out this test, and state whether you reject or fail to reject the null hypothesis. In computing the test statistic, be sure to indicate whether you are using “t” or “z”.

c. Given your answer to part b., are you vulnerable to a Type I or Type II error? Explain why in a single sentence.

d. Compute the p-value for this test. Compute this value “as though” you set up the original hypothesis as a 2-tailed test (no matter how you actually set it up). Interpret the meaning of the p-value in a single sentence.