.In a recent survey, police officers were asked if they believed that marijuana was a gateway drug. Of 919 officers who worked for county or parish sheriff's offices, 728 believed that marijuana was a gateway drug. Of 330 officers who worked for state police agencies, 257 believed that marijuana was a gateway drug. Use this information to calculate a 95% confidence interval for the difference in proportions of county (or parish) sheriff's officers and state troopers who believe marijuana is a gateway drug.

a. What is the sample statistic of interest. Provide notation and value.

b. Are the sample sizes large enough to use formulas based on the CLT?

c. Calculate the standard error using the formula based on the CLT (if the same sizes are large enough).

d. Calculate the 95% confidence interval.

e. Interpret the confidence interval in the context of the question.