Question

Tires: A tire manufacturer is considering a newly designed tire tread pattern for its all-weather tires. Tests have indicated that these tires will produce better gas mileage and longer tread life than the all-weather tires that the company currently sells. The last remaining test is for braking effectiveness. The company wants a car travelling 60 mph to come to a complete stop within an average of 125 feet after the brakes are applied. The company will adopt the new tread pattern unless there is strong evidence that tires with the new tread pattern have a braking distance of more than 125 feet. (Trials are as follows:)

Trial,Distance

1,129

2,128

3,130

4,132

5,135

6,123

7,120

8,125

9,128

10,130

11,127

12,129

13,131

14,133

15,136

16,122

17,119

18,124

19,129

20,127

a. State the null hypothesis and the alternative hypothesis that should be tested.

b. State and check model conditions for performing a t-test.

c. Compute the value of the t-statistic and also report the corresponding degrees of freedom and the p-value for the test.

d. State your conclusions in the context of the question that the company wants to answer. Be sure to link your conclusion to the p-value computed in part (c).

e. Construct a 95% confidence interval for the mean stopping distance for tires with the new tread pattern. What does this confidence interval indicate?

f. What is the margin of error for the confidence interval in part (e)? How many stopping trails would need to be done to cut this margin of error in half?

Answer 1