Question

a car company says that the mean gas mileage for its luxury sedan is at least 25 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 23 mpg and a standard deviation of 2 mpg. at \\( \alpha = 0.05 \\), test the company’s 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 be used and why? a. use a normal sampling distribution because the population is normal, and \\( \sigma \\) is unknown. b. use a t - sampling distribution because \\( n < 30 \\). c. use a normal sampling distribution because \\( n>30 \\). d. use a normal sampling distribution because the population is normal, and \\( \sigma \\) is known. e. use a t - sampling distribution because the population is normal, and \\( \sigma \\) is known. f. use a t - sampling distribution because the population is normal, and \\( \sigma \\) is unknown.

Explanation:

When the population is normally distributed, and the population standard deviation ($\sigma$) is unknown, we use the t - sampling distribution. Here, the sample size $n = 5<30$, the population is normal, and we are given the sample standard deviation (not the population standard deviation).

Answer:

F. Use a t - sampling distribution because the population is normal, and $\sigma$ is unknown.