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 6 cars has a mean gas mileage of 21 mpg and a standard deviation of 3 mpg. at \\( \alpha = 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 be used and why? o a. use a t - sampling distribution because \\( n<30 \\). o b. use a normal sampling distribution because \\( n>30 \\). o c. use a t - sampling distribution because the population is normal, and \\( \sigma \\) is unknown. o d. use a normal sampling distribution because the population is normal, and \\( \sigma \\) is unknown. o e. use a t - sampling distribution because the population is normal, and \\( \sigma \\) is known. o f. use a normal sampling distribution because the population is normal, and \\( \sigma \\) is known.

Explanation:

When the population is normally distributed and the population standard deviation ($\sigma$) is unknown, we use the t - sampling distribution. Here, the population is normally distributed (given in the problem) and we are only given the sample standard deviation ($s = 3$), so $\sigma$ is unknown.

Answer:

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