Confidence Interval Estimation

1. Compute a 90% confidence interval for the population mean, based on the sample 25, 27, 23, 24, 25, 24, and 59. Change the number from 59 to 24 and recalculate the confidence interval. Using the results, describe the effect of an outlier or extreme value on the confidence interval.

Hypothesis Testing

2. The director of admissions at the University of Maryland, University College is concerned about the high cost of textbooks for the students each semester. A sample of 45 students enrolled in the university indicates that X (bar) = $285.4 and s = $42.20.

a. Using the 0.05 level of significance, is there evidence that the population mean is above $300?

b. What is your answer in (a) if s = $90 and the 0.10 level of significance is used?

c. What is your answer in (a) if X (bar) = $310.10 and s = $40.20?

d. Based on the information in part (a), what decision should the director make about the books used for the courses if the goal is to keep the cost below $300?

3. A large hat manufacturer, MICHAELLA HATS, is concerned that the mean weight of their signature Kentucky Derby hat is not greater than 3.5 pounds. It can be assumed that the population standard deviation is .7 pounds based on past experience. A sample of 350 hats is selected and the sample mean is 3.25 pounds. Using a level of significance of .10, is there evidence that the population mean weight of the hats is greater than 3.5 pounds? Fully explain your answer.