Comfy Nights, a major international hotel chain, is interested in comparing the mean annual number of sick days taken by its employees in Paris and Sofia. In pursuit of this goal, they took a sample of 10 employees in Paris and 12 employees in Sofia and calculated the mean annual sick day usage. Assume that the annual number of sick days taken per employee is normally distributed in both cities.

	paris	sofia
sample mean	10.4	9.0
sample variance	2.5	3.4
sample size	10	12

a) Using a 5% significance level, test to see whether the population variance of the Sofia data is less than 3.6. b) Based on your conclusion in part a), what kind of error could you have made - Type I or Type 11? Explain briefly. c) Calculate a 90% confidence interval for the difference in the population mean annual number of sick days taken by the employees in the two cities. d) Using a 5% significance level, test to see whether the employees in Sofia take less annual sick days on average than do the employees in Paris. e) Based on your conclusion in part d), what kind of error could you have made - Type I or Type 1l? Explain briefly.