7.6

A leading researcher in the study of interstate highway accidents proposes that a major cause of many collisions on the interstates is not the speed of the vehicles but rather the difference in speeds of the vehicles. When some vehicles are traveling slowly while other vehicles are traveling at speeds greatly in excess of the speed limit, the faster-moving vehicles may have to change lanes quickly, which can increase the chance of an accident. Thus, when there is a large variation in the speeds of the vehicles in a given location on the interstate, there may be a larger number of accidents than when the traffic is moving at a more uniform speed. The researcher believes that when the standard deviation in speed of vehicles exceeds 10 mph, the rate of accidents is greatly increased. During a 1-hour period of time, a random sample of 50 vehicles is selected from a section of an interstate known to have a high rate of accidents, and their speeds are recorded using a radar gun. The data are presented here.

1. Does the data indicate that the standard deviation in vehicle speeds exceeds 10 mph? Use a = .05 in reaching your conclusion.

Hypothesis tests for variance/std dev;By hand chi-squared test statistic. Compare with value from SAS

Ho: Std. Deviation of vehicle > or = 10 mph (rate of accidents increased)(Claim)

Ha: Std. Deviation of vehicle < 10 mph (rate of accidents decreased)