2. Suppose your client wants to know if there is evidence of racial differ- ences in who gets stopped. Specifically, they want to know if Black people are stopped at a rate that is fundamentally different than the percentage of Black people living in New York City (about 24%).

To answer their question suppose that observations are independent and reflect a random sample from the data generating process that describes how the NYPD stops people. Now do the following:

(a) (10 points) What is the population of interest? What kind of distribution is it? What is the population parameter of interest?

(b) (2 points) Write down the null and alternative hypothesis for this test. Is it a one or two sided test?

(c) (2 points) Estimate the percentage of Black people stopped using the sample mean

HINT Create a new variable that is 1 if the person stopped is Black and 0 otherwise. Should you use mutate or mutate or summarize? You can also look up the ifelse function for this, you may find it helpful.

NOTE Black-Hispanic individuals are listed separately, be sure to count them in your answer

(d) (2 points) Estimate the standard error of this sample mean and describe the sampling distribution of this sample mean. (HINT: Does the central limit theorem apply? Do we need it?)

(e) (2 points) Is a t or z test more appropriate for this question? Does it matter? Why or why not?

(f) (2 points) Choose a level of from the set {0.01,0.05,0.10} to test the hypothesis justify your choice with a brief discussion of whether you are more concerned about a type I or type II error (1-2 sentences).

(g) (5 points) Conduct the test and interpret the results in context (1-2 sentences)

(h) (5 points) Explain why the assumption that "observations are in- dependent and reflect a random sample from the data generating process that describes how the NYPD stops people" is relevant and important for this analysis. (3-4 sentences)