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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.
A human resources manager is assessing the popularity of the current compensation plan. The manager collects two samples of 50 employees each from two different divisions in the company. In the first sample, 40 individuals indicated that they are in favor of the current plan. In the second sample, only 30 individuals indicated that they are in favor of the current plan. Conduct a hypothesis test at a 5 percent level of significance to determine whether the proportion in favor of the plan is significantly different between the two samples