Question

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, was recorded as follows:

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 two-sample t-test was used to compare the mean kilometers per liter for the two types of tires using a .05 level of significance. The resulting p-value was .0152.
State the null and alternate hypotheses, state whether the null hypothesis should be rejected or not rejected and your reason for that conclusion, state the meaning of that conclusion specifically in terms of the problem being studied.

Answer 1

Explanation:

Corresponding gasoline consumption when radial tires is used and gasoline consumption when regular belted tires is used form matched pairs.

The data for the test are the differences between the gasoline consumption when radial tires is used and gasoline consumption when regular belted tires is used.

μd = the gasoline consumption when radial tires is used minus the gasoline consumption when regular belted tires is used.

For the null hypothesis

H0: μd ≥ 0

For the alternative hypothesis

H1: μd < 0

The resulting p-value was .0152.

Since alpha, 0.05 > than the p value, 0.0152, then we would reject the null hypothesis. Therefore, at 5% significance level, we can conclude that the gasoline consumption when regular belted tires is used is higher than the gasoline consumption when radial tires is used.