A consumer group wants to know if an automobile insurance company with thousands of customers has an average insurance payout for all their customers that is greater than $500 per insurance claim. They know that most customers have zero payouts and a few have substantial payouts. The consumer group collects a random sample of 18 customers and computes a mean payout per claim of $579.80 with a standard deviation of $751.30.
Is it appropriate for the consumer group to perform a hypothesis test for the mean payout of all customers?
Yes, it is appropriate because the population standard deviation is unknown.
A
Yes, it is appropriate because the sample size is large enough, so the condition that the sampling distribution of the sample mean be approximately normal is satisfied.
B
No, it is not appropriate because the sample is more than 10 percent of the population, so a condition for independence is not satisfied.
C
No, it is not appropriate because the standard deviation is greater than the mean payout, so the condition that the sampling distribution of the sample mean be approximately normal is not satisfied.
D
No, it is not appropriate because the distribution of the population is skewed and the sample size is not large enough to satisfy the condition that the sampling distribution of the sample mean be approximately normal.
E
D?
No, it is not appropriate because the distribution of the population is skewed and the sample size is not large enough to satisfy the condition that the sampling distribution of the sample mean be approximately normal.
Yes, the correct answer is D.
It is not appropriate for the consumer group to perform a hypothesis test for the mean payout of all customers because the distribution of the population is skewed, and the sample size is not large enough to satisfy the condition that the sampling distribution of the sample mean be approximately normal. Additionally, the standard deviation being greater than the mean payout does not impact the appropriateness of the hypothesis test.
Yes, you are correct. The appropriate answer is D.
The reason is that the question mentions that "most customers have zero payouts and a few have substantial payouts," implying that the distribution of insurance payouts is likely to be skewed. In such cases, the condition that the sampling distribution of the sample mean be approximately normal may not be satisfied, unless the sample size is very large. Since the question states that the sample size is 18, which is considered small, this condition is not met.
Therefore, it is not appropriate for the consumer group to perform a hypothesis test for the mean payout of all customers in this situation.