A leading researcher in the study of interstate highway accidents proposes that a major...

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 100 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 summarized here and in a boxplot.

a. Does the boxplot suggest any violation of the conditions necessary to use the chi-square procedures for generating a confidence interval and a test of hypotheses about ?

b. Estimate the standard deviation in the speeds of the vehicles on the interstate using a 95% confidence interval.

c. Do the data indicate at the 5% level that the standard deviation in vehicle speeds exceeds 10 mph?