Question

Crash testing is a highly expensive procedure to evaluate the ability of an automobile to withstand a serious accident. A simple random sample of 13 small cars were subjected to a head-on collision at 40 miles per hour. Of them 8 were “totaled,” meaning that the cost of repairs is greater than the value of the car. Another sample of 17 large cars were subjected to the same test, and 5 of them were totaled. Let pX represent the population proportion of small cars that are totaled and let pY represent the population proportion of large cars that are totaled. Find a 95% confidence interval for the difference pX – pY . Round the answers to four decimal places.

Answer 1

-0.0205 < p1 - p2 < 0.6631

Explanation:

Here we need to use the formulas for a confidence interval using a difference of 2 given proportions.

Proportion 1 (small cars) = 8/13

Proportion 2 (large cars) = 5/17

A 95% confidence level has a z-score of 1.96 (the method of looking up z-scores doesn't change with using two proportions instead of 1)

See attached photo for formulas and solutions, and the construction of the confidence interval...