1. A consumer testing organization wants to know whether two brands of work shoes have equally long- lasting heels. Test show that 50 randomly selected worked wore out the heels of Brand X shoes, on average, in 96 days with standard deviation of 6.4 days, while 50 randomly selected workers wore out the heels of Brand Y shoes, on average, in 99 days with a standard deviation of 6.1 days.

(a) Test at level of significance α = 0.05 whether the difference between the two average wearing lives is significant.

(b) Compute the p-value and use it to decide whether the difference between the sample means is significant at the 0.05 level of significance.

2. A study was made of the number of gallons of gasoline purchased by customers for their automobiles at two gasoline stations. If 35 randomly selected purchases made in station A average 9.6 gallons with standard deviation of 1.75 gallons and 51 randomly selected sales at station B average 8.3 gallons with a standard deviation of 2.18, test at the level of significance α = 0.01 whether the difference between these two-sample means is significant.

3. Suppose that a delivery truck, while on its route on six randomly selected days, made an average of 14 deliveries per day with a standard deviation of 2 deliveries. A second delivery truck, while on another route on seven randomly selected days, made an average of 12 deliveries per day with a standard deviation of 4 deliveries. Can we assert at the level of significance α = 0.05 that the first delivery truck on its route makes a larger number of deliveries than the second delivery truck on its route?