An insurance company evaluates many variables about a person before deciding on an appropriate rate for automobile insurance. A representative from a local insurance agency selected a random sample of 15 insured drivers and recorded the amount of claims each made in the last 3 years. Based on this information, which of the following will you construct to learn about the average amount of claims made by the company's customer?
A) confidence interval estimate for the mean using the standard normal distribution
B) confidence interval estimate for the mean using the Student's t distribution
C) confidence interval estimate for the proportion using the standard normal distribution
D) confidence interval estimate for the difference between two means using the standard normal distribution

Question

Quizplus · Accepted Answer

Since the sample size is small (n = 15), we cannot rely on the assumption that the population is normally distributed, so we need to use the Student's t distribution. We are interested in estimating the average amount of claims made by the company's customers, so we want to construct a confidence interval estimate for the mean. Therefore, option B is the best choice. Option A is incorrect because we cannot use the standard normal distribution due to the small sample size. Option C is incorrect because we are not interested in the proportion of customers who made a claim, but the average amount of claims made. Option D is incorrect because there is no mention of comparing two means in the problem.

An Insurance Company Evaluates Many Variables About a Person Before