Question

Do out-of-state motorists violate the speed limit more frequently than in-state motorists? This vital question was addressed by the highway patrol in a large eastern state. A random sample of the speeds of 2,500 selected cars was categorized according to whether the car was registered in the state or in some other state and whether or not the car was violating the speed limit. The data follow.

In state speeding cars: 521

Out of state speeding cars: 328

In state not speeding cars: 1141

Out of state not speeding cars: 510

a.) Do these data provide enough evidence to support the highway patrol's claim at the 5% significance level? Your conclusion must be in terms of the P-Value. Show all necessary work.

b). What type of error is possible and describe this error in terms of the problem?

c). Estimate the difference in the actual percentage of In State and Out of State speed limit violators using a 95% confidence interval. Show all necessary work. Using this interval estimation, is there sufficient evidence to support the highway patrol's claim? Explain Carefully.

d). Carefully interpret the confidence interval estimation.

Use non-parametrics/Mann-Whitney test if the problem calls for it- Does it?

Answer 1

No, we don't require Mann whiteny test here because assumptions of normality are satisfied by both samples i.e. sample sizes are large enough and also they satisfy condition of : np>=10 .