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 24 trucks were fitted with the new fuel injection system and driven under different conditions. For these trucks, the sample variance of gasoline consumption was 56.3. Another random sample of 41 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 39.8. Test the claim that there is a difference in population variance of gasoline consumption for the two injection systems. Use a 5% level of significance. How could your test conclusion relate to the question regarding the consistency of fuel consumption for the two fuel injection systems? (a) What is the level of significance? State the null and alternative hypotheses. (b) Find the value of the sample F statistic. What are the degrees of freedom? What assumptions are you making about the original distribution? (c) Find or estimate the P-value of the sample test statistic. (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? (e) Interpret your conclusion in the context of the application. Step 1 (a) What is the level of significance? State the null and alternative hypotheses. Recall that an F-distribution is used to test a hypothesis about two variances. To test with a 5% level of significance, we set a = Note that since we have two populations, we will define population 1 to correspond to the larger sample variance. The sample variance of gasoline consumption for the new fuel injection system is 56.3, and 39.8 for the old system, so the new system will be population 1. 2 Then, 2 is the population variance for the new system and ₂² is the population variance for the old system. We want to know if there is evidence to suggest that there is a difference between these two variances. Therefore, we use the following null and alternative hypotheses. Ho:1 ? O H₂:0 ?