Crash Data The Insurance Institute for Highway Safety conducts experiments in which cars are crashed into a fixed barrier at 40 mph. The barrier’s deformable face is made of aluminum honeycomb, which makes the forces in the test similar to those involved in a frontal offset crash between two vehicles of the same weight, each going just less than 40 mph. Suppose you want to know if the mean head injury resulting from this offset crash is the same for large family cars, passenger vans, and midsize utility vehicles. The researcher wants to determine if the means for head injury for each class of vehicle are different. The following data were collected from the institute’s study.

(a) State the null and alternative hypotheses.

(b) Verify that the requirements to use the one-way ANOVA procedure are satisfied. Normal probability plots indicate that the sample data come from normal populations.

(c) Test the hypothesis that the mean head injury for each vehicle type is the same at the level of significance.

(d) Draw boxplots of the three vehicle types to support the analytic results obtained in part (c).

 

Suppose a large insurance company wants to estimate the difference between the average amount of term life insurance purchased per family and the average amount of whole life insurance purchased per family. To obtain an estimate, one of the company’s actuaries randomly selects 27 families who have term life insurance only and 29 families who have whole life policies only. Each sample is taken from families in which the leading provider is younger than 45 years of age. Use the data obtained to construct a 95% confi dence interval to estimate the difference in means for these two groups. Assume the amount of insurance is normally distributed.