A car company says that the mean gas mileage for its luxury sedan is at least 22 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 $5 mpg$ . At $α = 0.05$ , 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 $n > 30$ .
C. Use a t-sampling distribution because the population is normal, and $σ$ is known.
E. Use a normal sampling distribution because the population is normal, and $σ$ is known.
B. Use a normal sampling distribution because the population is normal, and $σ$ is unknown.
D. Use a t-sampling distribution because the population is normal, and $σ$ is unknown.
F. Use a t-sampling distribution because $n < 30$ .

Answer

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Answer

Final Answer: \boxed{\text{D. Use a t-sampling distribution because the population is normal, and } \sigma \text{ is unknown.}}

Steps

Step 1 ：The question is asking which sampling distribution should be used given the information provided.

Step 2 ：The sample size is less than 30, the population is normally distributed, and the population standard deviation is unknown.

Step 3 ：Therefore, we should use a t-sampling distribution because the population is normal, and the standard deviation is unknown.

Step 4 ：This is because the t-distribution is typically used when the sample size is small and the population standard deviation is unknown.

Step 5 ：Final Answer: \boxed{\text{D. Use a t-sampling distribution because the population is normal, and } \sigma \text{ is unknown.}}