Question

The mayor of a city claims that racial profiling is not a problem in his city. A civil rights group disagrees. The proportion of Caucasians who have been stopped while driving, without good reason, at least once in the past year is 0.19 (19%). In a random sample of 340 African Americans , the proportion who have been stopped is 0.37 (37%). Assuming that the proportion of all African Americans in the city that have been stopped is 0.19, the probability of selecting a sample in which the proportion who have been stopped is 0.37 or more is less than 0.001.Discuss whether the sample provides evidence for rejecting the null hypothesis

Answer 1

Let, p = proportion of African Americans who have been stopped while driving at least once in the past year.

To test whether there is a significant difference in results from the survey, the z test for the one proportion is used since the sample data values satisfy the normality condition

Hypotheses

The null and alternative hypotheses are defined as,

This is a right-tailed test

Let the significance level = 0.05

P-value

Given: P-value < 0.001

Conclusion

Since the p-value is less than the significance level, the null hypothesis is rejected hence there is sufficient evidence to conclude the proportion of African Americans who have been stopped while driving at least once in the past year is greater than 0.19

Explanation

The p-value is the probability of rejecting the null hypothesis when it is actually true such it is the probability of incorrectly rejecting the null hypothesis. In this context, the p-value is the probability that the proportion of African Americans who have been stopped while driving at least once in the past year is greater than 0.19 while actually it is not greater than 0.19. This probability is less than 0.001 which is very less likely hence we can reject the null hypothesis.