Question

Question 5. (Two Variances)A new fuel injection system has been engineered for pickup trucks. The new system and the old system both produce about the same average miles per gallon. However, engineers question which system (old or new) will give better consistency in fuel consumption (miles per gallon) under a variety of driving conditions. A random sample of 31 trucks were fitted with the new fuel injection system and driven under different conditions. For these trucks, the sample variance of gasoline consumption was 58.4. Another random sample of 25 trucks were fitted with the old fuel injection system and driven under a variety of different conditions. For these trucks, the sample variance of gasoline consumption was 31.6. Test the claim that there is a difference in population variance of gasoline consumption for the two injection systems. Perform this test by hand and be sure to show full details. Use a 5% level of significance. (15 points)

Answer 1

We will conduct a F-test to check the difference in variances. THe hypothesis is:

Ho: σ12 = σ22
Ho: σ12 =/ σ22

Let's calculate the F-statistic:

F = s21 / s22

F = 58.4/31.6 = 1.848

The degrees of freedom are: (n1 - 1, n2 - 1) = (30, 24)

F-critical value at 5% significance level = 1.939

As the F-statistic = 1.848 < 1.939, we fail to reject the null hypothesis. Hence, we can say that there is no significant difference in the population variances of gasoline consumption for the two injection systems.