Low-profile tires are automobile tires that have a short sidewall height, which is the distance between the tire rim and the road. These tires provide better performance at the expense of gas mileage. The Ford Taurus was chosen to measure the effect these tires have on gas mileage. Ten cars of this model were selected, and the gas mileage obtained on one tank of gas was measured with standard tires. Lowprofile tires were then installed on the same cars. Using the same drivers, the gas mileage was again recorded. The results are shown as follows and can be found in the Excel file low profile.xlsx. Assume the population variances are equal.

Car Standard Low Profile Car Standard Low Profile 1 21.5 22.4 6 26.5 19.0 2 22.3 20.1 7 25.5 19.7 3 25.6 24.0 8 19.5 16.2 4 19.3 19.5 9 23.9 21.4 5 22.3 21.7 10 22.9 22.4

a. Using a = 0.05, perform a hypothesis test to determine if the average gas mileage obtained using standard tires is higher than the average gas mileage obtained using low-profile tires.

b. Approximate the p-value using Appendix A and interpret the result.

c. Construct a 90% confidence interval to estimate the average difference in gas mileage obtained using these two types of tires. Interpret the results.

d. Verify your results using Excel or PHStat.

e. Identify the p-value using Excel and interpret the result.

f. What assumptions need to be made in order to perform this procedure?

AppendixLO1