1- A Drug Company develops a new drug, designed to prevent colds. The company states that the proportion of drug effectiveness for men is the same as that for women. To test this claim, they choose a random sample of 100 women and 200 men. At the end of the study, 38% of the women caught a cold; and 51% of the men caught a cold. Based on these findings, can we reject the company's claim that drug effectiveness is the same for men and for women? Use a 0.05 level of significance

2- Find the 90% confidence interval for the variance and standard deviation for the time it takes a state police inspector to check a truck for safety if a sample of 27 trucks has a standard deviation of 6.8 minutes. Assume the variable is normally distributed.

3- A researcher suggests that male nurses earn more than female nurses. A survey of 16 male nurses and 20 female nurses reports these data. Usea = 0.01

Female	Male
s2 = $250	s1 = $300
n2 = 20	n1 = 16

a) Test to check if variances are equal?

b) According to your answer in part (a); test if the average amount earned by males is more than that earned by females.

4- A researcher wishes to estimate within $300 the true average amount of money a county spends on roads repairs each year. If she wants to be 90% confident, how large a sample is necessary? The standard deviation is known to be $900.