You are the automotive specialist for the monthly magazine Consumer Beware. Part

Question

You are the automotive specialist for the monthly magazine Consumer Beware. Part of your job is to investigate the claims made by automakers in their TV commercials. You are particularly suspicious of a new economy car that the automaker claims will get 78 miles per gallon. After checking the mileage figures for a random sample of 125 owners of this car, you find an average “miles per gallon” of 75.5, with a standard deviation of 3.7. At the 99% level, do your results tend to confirm or refute the manufacturer’s claims?

Explanation / Answer

The population standard deviation is unknown, therefore, the test statistic is as follows:

t=(Xbar-mu)/(s/sqrt n-1), where Xbar is sample mean, mu is the population mean, s is the sample standard deviation and n is the sample size.

t124=(75.5-78)/(3.7/sqrt 125-1)=-7.524.

The p value at alpha=0.01 is 0.0000

The p value is less than 0.01, therefore, reject the null hypothesis.to confirm the manufacturer's claim.

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