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# Question 7 (15 marks) SECTION 3 A car manufacturer states that its new model does 32.5 miles per gallon (mpg). A recent independent study of 50 of the new cars showed a mean mpg of only 30.4 with a...

Question 7 (15 marks)

SECTION 3

A car manufacturer states that its new model does 32.5 miles per gallon (mpg). A recent independent study of 50 of the new cars showed a mean mpg of only 30.4 with a standard deviation of 5.3 mpg. Test the view that the manufacturerâ€™s claim is too high using a 1% level of significance (1% critical value for Z = -2.33).

Question 8 (15 marks)

The expected life of a car engine in an electric car is claimed to be 90,000 miles. A sample of 190 electric cars gives a mean life of 96,700 miles with a standard deviation of 37,500 miles. Test whether the electric cars are lasting longer than expected at the 1% level of significance (1% critical value for Z = -2.33).

Answered 5 days After May 03, 2022

## Solution

Robert answered on May 09 2022
The null and alternative hypotheses are
H0: Î¼=32.5
Ha: Î¼>32.5 â€‹
Here, the significance level is Î±=0.01, and the critical value for a right-tailed test is tc=2.405
The rejection region is R={t:t>2.405}
The t-statistic is

Clearly, t=âˆ’2.802â‰¤tc=2.405, it is then concluded that the null...
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