An unmarried 19-year-old who has just purchased his/her own 2-year-old Honda Civic might be asking,“Why does auto insurance cost so much?”There are many reasons, according to the insurance agent, one of which is whether the driver is male or female. The insurance rates listed below are for a random sample of 16 ZIP codes within a 50-mile radius of our 19-year-old in question. The data are for a policy whose features are $500 deductible, $25,000/$50,000 bodily injury, $25,000 property, and $25,000/$50,000 uninsured/underinsured motorist.
a. At first glance, does there seem to be a pattern to the relationship between the insurance premiums for males and females? Describe it.
b. Graphically describe each set of data—males, females, and difference—using a histogram and one other graph.
c. Find the mean and the standard deviation for each set of data: males, females, and difference.
d. Are the assumptions for a mean of a paireddifference confidence interval satisfied? Explain.
e. Using a 95% confidence interval, estimate the mean of the differences.Write a complete confidence interval statement.
f. Do your answers to the above questions suggest any evidence of a difference between the auto insurance rates for male and female 19-year-old drivers? Explain.