A new fuel injection system has been engineered for pickuptrucks. The new system and the old system both produce about thesame average miles per gallon. However, engineers question whichsystem (old or new) will give better consistency in fuelconsumption (miles per gallon) under a variety of drivingconditions. A random sample of 41 trucks were fitted with the newfuel injection system and driven under different conditions. Forthese trucks, the sample variance of gasoline consumption was 53.Another random sample of 21 trucks were fitted with the old fuelinjection system and driven under a variety of differentconditions. For these trucks, the sample variance of gasolineconsumption was 33.1. Test the claim that there is a difference inpopulation variance of gasoline consumption for the two injectionsystems. Use a 5% level of significance. How could your testconclusion relate to the question regarding theconsistency of fuel consumption for the two fuel injectionsystems?

(a) What is the level of significance?


State the null and alternate hypotheses.

H_o: σ₁² =σ₂²; H₁:σ₁² >σ₂²H_o:σ₁² >σ₂²; H₁:σ₁² =σ₂²Â Â Â Â H_o:σ₂² =σ₁²; H₁:σ₂² >σ₁²H_o:σ₁² =σ₂²; H₁:σ₁² ≠σ₂²

(b) Find the value of the sample F statistic. (Round youranswer to two decimal places.)


What are the degrees of freedom?

dfN
dfD

What assumptions are you making about the originaldistribution?

The populations follow independent normal distributions. We haverandom samples from each population.The populations followdependent normal distributions. We have random samples from eachpopulation.    The populations followindependent normal distributions.The populations follow independentchi-square distributions. We have random samples from eachpopulation.

(c) Find or estimate the P-value of the sample teststatistic.

P-value > 0.2000.100 < P-value <0.200    0.050 < P-value <0.1000.020 < P-value < 0.0500.002 <P-value < 0.020P-value < 0.002

(d) Based on your answers in parts (a) to (c), will you reject orfail to reject the null hypothesis?

At the α = 0.05 level, we reject the null hypothesisand conclude the data are not statistically significant.At theα = 0.05 level, we reject the null hypothesis and concludethe data are statistically significant.    Atthe α = 0.05 level, we fail to reject the null hypothesisand conclude the data are not statistically significant.At theα = 0.05 level, we fail to reject the null hypothesis andconclude the data are statistically significant.

(e) Interpret your conclusion in the context of theapplication.

Fail to reject the null hypothesis, there is sufficient evidencethat the variance in consumption of gasoline is greater in the newfuel injection systems.Reject the null hypothesis, there isinsufficient evidence that the variance in consumption of gasolineis greater in the new fuel injectionsystems.    Reject the null hypothesis, thereis sufficient evidence that the variance in consumption of gasolineis different in both fuel injection systems.Fail to reject the nullhypothesis, there is insufficient evidence that the variance inconsumption of gasoline is different in both fuel injectionsystems.