The daily wages in a particular industry are normally distributed with a mean of $94 and a standard deviation of $11.88. Suppose a company in this industry employs 40 workers and pays them $91.50 per week on the average. Can these workers be viewed as a random sample from among all workers in the industry?

a. What are the null and alternative hypotheses to be tested?

b. Use the Large-Sample Test of a Population Mean applet to find the observed value of the test statistic.

c. Use the Large-Sample Test of a Population Mean applet to find the p-value for this test.

d. If you planned to conduct your test using α = .01, what would be your test conclusions?

e. Was it necessary to know that the daily wages are normally distributed? Explain your answer.