1. Management of the Stanley Steel company wish to compare the performance of day and evening shift workers. A sample of 10 day shift workers yielded a mean output of 74.3 parts per hour with a standard deviation of 8, while a sample of 20 evening shift workers yielded a mean of 67.7 with a standard deviation of 16. It may be assume that output on both the day and evening shifts is normally distributed.
(a) Calculate the ratio of the maximum sample variance to the minimum sample variance. Does it appear that the population variances are equal or unequal? Explain.
(b) Construct the appropriate 95% confidence interval for the difference in the mean output during the day and evening shifts, and interpret your result. Give clear definitions of the two population means.
(c) Suppose that the standard deviation on the evening shift was 12, and not 16. How would you compute the confidence interval in (b)? Just give the formula, and plug in all the appropriate values; it is not necessary to actually calculate the interval.
(d) If output on the shifts were not normally distributed, would your interval in (b) still be valid? Explain.
2. A consumer interest group is concerned about rising prices for home in the Toronto real estate market. A random sample of 100 recently sold homes in Toronto yielded an average selling price of $428,900. Assume that the population standard deviation of the selling price of a home in Toronto is $67,500. At the 5% level of significance, is there enough evidence to indicate that the average selling price of all homes in Toronto exceeds $400,000? Under what conditions is this result valid?