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

Answer a)

We will be using z test for two proportion to test the claim.

Let p1 represents proportion of out of state speeding car

Let p2 represents proportion of in state speeding car

Thus, it can be said that there is enough evidence to support the highway patrol's claim at the 5% significance level

Answer b)

In statistical hypothesis testing a type I error is the rejection of a true null hypothesis. . Thus, in this case Type I error is possible as null hypothesis is reject.

In this problem Type I error is rejecting null hypothesis even when true proportion of out of state speeding cars is less than or equal to true proportion of in state speeding cars.

Answer c)

Zero is the null value of the parameter (in this case the difference in proportions). If a 95% confidence interval does not includes the null value, then there is statistically meaningful or statistically significant difference between the two proportions. In addition, since difference in positive there is sufficient evidence to support the highway patrol's claim.

Answer d)

Based on the data provided, the 95% confidence interval for the difference between the population proportions of out of state speeding cars and in state speeding cars is 0.038<p<0.118, which indicates that we are 95% confident that the true difference between population proportions is contained by the interval (0.038,0.118).