11.18 The paper “The Observed Effects of Teenage Passengers on the Risky Driving Behavior of Teenage Drivers”

(Accident Analysis and Prevention [2005]: 973– 982)

investigated the driving behavior of teenagers by observing their vehicles as they left a high school parking lot and then again at a site approximately 12 mile from the school. Assume that it is reasonable to regard the teen drivers in this study as representative of the population of teen drivers. Use a .01 level of significance for any hypothesis tests.

a. Data consistent with summary quantities appearing in the paper are given in the accompanying table. The measurements represent the difference between the observed vehicle speed and the posted speed limit (in miles per hour) for a sample of male teenage drivers and a sample of female teenage drivers. Do these data provide convincing support for the claim that, on average, male teenage drivers exceed the speed limit by more than do female teenage drivers?

Amount by Which Speed Limit Was Exceeded Male Driver Female Driver 1.3 20.2 1.3 0.5 0.9 1.1 2.1 0.7 0.7 1.1 1.3 1.2 3 0.1 1.3 0.9 0.6 0.5 2.1 0.5

b. Consider the average miles per hour over the speed limit for teenage drivers with passengers shown in the following table. For purposes of this exercise, suppose that each driver-passenger combination mean is based on a sample of size n 5 40 and that all sample standard deviations are equal to .8.

Male Passenger Female Passenger Male Driver 5.2 .3 Female Driver 2.3 .6 i. Is there sufficient evidence to conclude that the average number of miles per hour over the speed limit is greater for male drivers with male passengers than it is for male drivers with female passengers?

ii. Is there sufficient evidence to conclude that the average number of miles per hour over the speed limit is greater for female drivers with male passengers than it is for female drivers with female passengers?

iii. Is there sufficient evidence to conclude that the average number of miles per hour over the speed limit is smaller for male drivers with female passengers than it is for female drivers with male passengers?

c. Write a few sentences commenting on the effects of gender on teenagers driving with passengers.