A car company claims that the mean gas mileage for its luxury sedan is at least 24 miles per gallon. A random sample of 7 cars has a mean gas mileage of 23 miles per gallon and a standard deviation of 1.1 miles per gallon. At α=0.05, can you support the company's claim assuming the population is normally distributed?

Question

Vanessa Rangel

Mathematics

2 December, 12:25

A car company claims that the mean gas mileage for its luxury sedan is at least 24 miles per gallon. A random sample of 7 cars has a mean gas mileage of 23 miles per gallon and a standard deviation of 1.1 miles per gallon. At α=0.05, can you support the company's claim assuming the population is normally distributed?

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Zane · Answer 1

a) t sampling distribution because B the population is normal, and standard deviation is unknown

b) H0: mu < = 21

HA mu > 21

alpha = 0.05

t critical value at 4 df and alpha 0.05 is 2.132

The rejection region is t > 2.132

t = (xbar - µ) / (s/√n)

t = (19 - 21) / (4/√5)

t = - 2 / (4/2.2361)

t = - 1.118

t does not fall into the rejection region, so we have insufficient evidence to reject the null hypothesis. The claim cannot be verified.

We tested the manufacturer's claim that the mean mpg is greater than 21, at alpha = 0.05. We used a one-tailed one-sample t-test (4 df). We placed the rejection region in the right tail of the t-distribution because we were only interested in the claim that the mileage was more than 21. The test result showed that the claim could not be validated. The sample mean was 19, which was less than the claim, so no calculations were needed to reject the null hypothesis. We were not able to find that the mean was statistically greater than 21.