A taxi company manager is trying to decide whether the use of radial tires instead of regular belted tires improves fuel economy. Twelve cars were equipped with radial tires and driven over a prescribed test course. Without changing drivers, the same cars were then equipped with regular belted tires and driven once again over the test course. The gasoline consumption, in kilometers per liter, is shown in the table below. Kilometers per Liter
Car Radial Tires Belted Tires
1 4.2 4.1
2 4.7 4.9
3 6.6 6.2
4 7.0 6.9
5 6.7 6.8
6 4.5 4.4
7 5.7 5.7
8 6.0 5.8
9 7.4 6.9
10 4.9 4.7
11 6.1 6.0
12 5.2 4.9
a. Assuming that distribution of differences in kilometers per liter is approximately normal, can we conclude that cars equipped with radial tires give better fuel economy than those equipped with belted tires? Use a .05 level of significance.
Complete the following:
1. State H0.
2. State H1.
3. State the value of α.
4. State the value of the test statistic.
5. State the p-value.
6. State the decision in terms of H0 and why.
7. State the decision in terms of the problem.
b. Construct a 95% confidence interval estimate of the difference in kilometers per liter. Do the results of parts (a) and (b) agree? Explain why or why not.
c. Suppose you use a .01 level of significance instead of a .05 level. Without doing the problem again, would the result be different from that in part (a). Explain your answer.
d. Is it important that the same cars were driven with both radial and belted tires, that drivers didn't change when the belted tires replaced the radial tires, and that the same course was used in all tests? Explain why or why not.