Question: A manufacturer has received complaints that aging production equipment is forcing workers to work overtime in order to meet production quotas. Historically, the average hours worked per week at the company is normally distributed, with a mean of 40 hours and a standard deviation of 7.5 hours. If a sample of 30 workers found an average work week of 45 hours, conduct a hypothesis test to determine if there is significant evidence (at a 5 percent level of significance) that the length of the average work week has increased.

State the hypothesis, the test statistic, the conclusion, (what you are accepting or rejecting) and make sure you answer the question.