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. 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. No, it is not appropriate because the sample is more than 10 percent of the population, so a condition for independence is not satisfied. 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. 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.
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
Is it appropriate for the consumer group to perform a hypothesis test for the mean payout of all customers?
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Yes, it is appropriate because the population standard deviation is unknown.
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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. -
No, it is not appropriate because the sample is more than 10 percent of the population, so a condition for independence is not satisfied.
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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.
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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.
Given:
From the provided information, it is known that the population is skewed as most of customers have zero payouts and a few have substantial payouts.
Also the sample size is 18 which is less than 30.
For normal approximation the sample size should at least 30.
Therefore, it is not appropriate to perform a hypothesis test for mean payout of all customers as the population is skewed and sample size is not enough to satisfy the normality condition.
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