A car manufacturer wishes to advertise that one of its models achieves over 30mp

Question

A car manufacturer wishes to advertise that one of its models achieves over 30mpg and carries out a fuel efficiency test to test this claim. Twenty cars of this particular model are randomly selected and driven by a nonprofessional driver from Phoenix to Dallas. The average gas mileage of the 20 cars is 30.0 mpg, with a standard deviation of 1.2 mpg. Assuming that the fuel efficiency is normally distributed under these circumstances, based on this sample can the car manufacterer advertise that this model gets over 30 mph? Carry out a hypothesis test to answer this question. Use a = 0.05. Clearly show all steps of your hypothesis test.

Explanation / Answer

Hypotheses:

H0: mu<=30 ( The average gas mileage is atmost 30mpg)

H1:mu>30 (The gas mileage is over than 30 mpg)

Distribution.:

For small sample size, (n<30) and population standard deviation unknown, use 1-sample t test.

For alpha=0.05 (one-tailed), abd df=19 (n-1), the critical t is:1.729.

Test statistic:

t=(Xbar-mu)/(s/sqrt N)

=(30-30)/(1.2/sqrt 20)

=0

Decision rule: Reject H0, if t>1.729.

Conclusion. The t test statistic do not fall in critical region, therefore, fail to reject null hypothesis. There is insufficient sample evidnce to support the claim of the manufacturer.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.