The manager of a manufacturing plant wants to test to see if her suspicions are correct that employees are not as productive on Fridays as on other days of the week. She has determined that the average units of production per worker are 58 per day for Mondays to Thursdays. She randomly selects a sample of 50 workers and gathers the data for the number of units they each produce over a random selection of Fridays.

a. If a hypothesis test were conducted at the 0.05 level of significance to test the null hypothesis that the mean number of units produced on Fridays is not less than 58 (i.e., H_o: 58; H_a: < 58) and the null hypothesis was not rejected, explain what type of error may have been made?

b. Explain at least one implication of making this error for the organization.

c. Explain how she will know if she made the error which is indicated above.

d. In discussing this issue with the manager of another plant, the other manager suggests a different approach to studying this issue. She suggests that the manager take a random sample of workers and gather data about the number of units each worker produces on Friday and the number of units the same workers produce on another day of the week. Indicate and explain what hypotheses test would be used with these data to determine if there is a mean difference in the number of units produced on Fridays and on other days of the week.

e. Indicate the hypotheses that would be used for the hypothesis test in part c to determine if there are fewer units produced on Fridays. (Express symbolically) H₀: H_A: