Question

A car company says that the mean gas mileage for its luxury sedan is at least 23 miles per gallon (mpg). You believe the claim is incorrect and find that a random sample of 7 cars has a mean gas mileage of 21 mpg and a standard deviation of 4 mpg. At α-010, test the company's claim. Assume the population is normally distributed. here to view 1 of the normal Which sampling distribution should be used and why? O A. Use a t-sampling distribution because n <30 O C. Use a normal sampling distribution because n>30 0 B. D. ° F. Use a t-sampling distribution because the population is normal, and σ is known. Use a normal sampling distribution because the population is normal, and σ is unknown. Use a t-sampling distribution because the population is normal, and σ is unknown. E. Use a normal sampling distribution because the population is normal, and σ is known. State the appropriate hypotheses to test. A. Ho: μ-23 На: #23 B. Ha.μ 23 Ha: μ> 23 D. Ho: μ 223 H, μ = 23 What is the value of the standardized test statistic? The standardized test statistic is (Round to two decimal places as needed.) What is the critical value? The critical value is (Round to three decimal places as needed.) What is the outcome and the condlusion of this test? HO. At the 10% significance level, there is evidence to Vthe car company's claim that the mean gas mileage for the luxury sedan is at least 23 miles per gallon.

Answer 1

Use t sampling distribution because population is normal and $\sigma$ is unknown.

The null and alternative hypothesis are

H0: $\mu$ >= 23

Ha: $\mu$ < 23

Test statistics

t = $\bar{x}$ - $\mu$ / S / sqrt(n)

= 21 - 23 / 4 / sqrt(7)

= -1.32

t critical value at 0.10 level with 6 df = -1.44

Since test statistics > -1.44, we do not have sufficient evidence o reject H0.

We conclude that,

Fail to reject H0. At the 10% significance level, there is insufficient evidence to support the car company's claim

that the mean mileage for the laxuary sedan is at most 23 miles per gallon.