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. 56.1 57.0 53.9 50.2 54.2 47.9 78.1 60.2 47.4 68.8 45.5 63.3 59.7 74.3 61.4 58.7 61.2 64.7 64.3 48.2 57.7 72.1 72.0 67.6 47.6 65.9 72.3 55.7 55.0 75.2 62.8 47.0 48.1 62.9 64.0 80.6 51.2 53.7 53.3 58.3 68.2 69.5 51.8 68.8 63.8 61.8 59.3 63.6 54.7 59.9 a. Do the data indicate any violations in the conditions necessary to use the chi-square procedures for generating confidence intervals and testing hypotheses? b. Estimate the standard deviation in the speeds of the vehicles traveling on the interstate using a 95% confidence interval. c. Do the data indicate that the standard deviation in vehicle speeds exceeds 10 mph? Use a 5 .05 in reaching your conclusion. d. To what population can the inferences obtained in parts (b) and (c) be validly applied?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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.
| 56.1 | 57.0 | 53.9 | 50.2 | 54.2 | 47.9 | 78.1 | 60.2 | 47.4 | 68.8 |
| 45.5 | 63.3 | 59.7 | 74.3 | 61.4 | 58.7 | 61.2 | 64.7 | 64.3 | 48.2 |
| 57.7 | 72.1 | 72.0 | 67.6 | 47.6 | 65.9 | 72.3 | 55.7 | 55.0 | 75.2 |
| 62.8 | 47.0 | 48.1 | 62.9 | 64.0 | 80.6 | 51.2 | 53.7 | 53.3 | 58.3 |
| 68.2 | 69.5 | 51.8 | 68.8 | 63.8 | 61.8 | 59.3 | 63.6 | 54.7 | 59.9 |
a. Do the data indicate any violations in the conditions necessary to use the chi-square procedures for generating confidence intervals and testing hypotheses?
b. Estimate the standard deviation in the speeds of the vehicles traveling on the interstate using a 95% confidence interval.
c. Do the data indicate that the standard deviation in vehicle speeds exceeds 10 mph? Use a 5 .05 in reaching your conclusion.
d. To what population can the inferences obtained in parts (b) and (c) be validly applied?
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