Question

A certain county is 25​% African American. Suppose a researcher is looking at jury​ pools, each with 200 ​members, in this county. The null hypothesis is that the probability of an African American being selected into the jury pool is 25​%. a. How many African Americans would the researcher expect on a jury pool of 200 people if the null hypothesis is​ true? b. Suppose pool A contains 17 African American people out of 200​, and pool B contains 39 African American people out of 200. Which will have a smaller​ p-value and​ why?

Answer 1

a. The researcher would expect 50 African Americans on a jury pool of 200 people if the null hypothesis is true. b. Pool A will have a smaller p-value because its observed proportion is less extreme.

Step-by-step explanation:

a. To calculate the expected number of African Americans on a jury pool of 200 people given the null hypothesis, we multiply the proportion of African Americans (0.25 or 25%) by the total number of people in the pool (200). Therefore, the expected number of African Americans would be 0.25 * 200 = 50.

b. To determine which pool will have a smaller p-value, we need to conduct a hypothesis test for each pool. The p-value represents the probability of obtaining a sample proportion as extreme or more extreme than the observed proportion, assuming the null hypothesis is true. Since the observed proportion in pool A (17/200 = 0.085) is less extreme than the observed proportion in pool B (39/200 = 0.195), pool A will have a smaller p-value.

Answer 2

Answer: a. 50 African Americans

b. Pool B will have a smaller​ p-value because that pool's number of AA people is further from the hypothesized number of AA people.

Step-by-step explanation: