A car company says that the mean gas mileage for its luxury sedan is at least 21

Question

A car company says that the mean gas mileage for its luxury sedan is at least 21 miles per gallon (mpg). You believe the claim is incorrect and find that a random sample of 5 cars has a mean gas mileage of 19 mpg and a standard deviation of 3 mpg. At a *0.10, test the companys claim. Assume the population is normally distributed. Click here to view the t distribution table. Click here to view page 1 of the normal table. Click here to view page 2 of the normal table. which sampling distribution should betsed and why? O A. Use a normal sampling distribution because the population is O B. Use a t-sampling distribution because the population is normal, and normal, and o is unknown. a is known. O C. Use a normal sampling distribution because n 30. O D. Use a t-sampling distribution because n

Explanation / Answer

Which sampling distribution should be used and why?

F. Use a t-sampling distribution because the population is normal and s is unknown.

State the appropriate hypothesis to test:

A. Ho: µ 21

Ha: µ < 21

What is the appropriate hypothesis to test:

t = (x bar - µ)/(s/sqrt(n))

= (19 -21)/(3/sqrt(5))

= -1.49

The standardized test statistics is -1.49

What is the critical value?

The critical value is -1.533

What is the outcome and conclusion of the test?

Fail to reject the null hypothesis and at 10% level of significance there is sufficient evidence to conclude that the mean gas mileage for its luxury sedan is at least 21 miles per gallon (mpg).

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