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Chapter 8: Problem 18

St. Louis County is \(24 \%\) African American. Suppose you are looking at jury pools, each with 200 members, in St. Louis County. The null hypothesis is that the probability of an African American being selected into the jury pool is \(24 \%\). a. How many African Americans would you expect on a jury pool of 200 people if the null hypothesis is true? b. Suppose pool A contains 40 African American people out of 200 , and pool B contains 26 African American people out of 200 . Which will have a smaller p-value and why?

Short Answer

Expert verified
a) Expect 48 African-Americans on the jury pool if the null hypothesis is true. b) Pool B will have a smaller p-value because its observed number of African Americans is further from what we would expect if the null hypothesis were true.

Step by step solution

01

Calculate the expected number of African Americans

To find out the expected number of African Americans in a jury pool of 200, one needs to apply the principle of probability. If the null hypothesis holds true, then the number of African-Americans expected can be calculated as 24% of 200 (the size of the jury pool). Calculate this as follows: \(0.24 * 200 = 48\). Hence, expect 48 African-Americans under the null hypothesis.
02

Compare observed African-Americans in jury pools A and B to expected number

In pool A, we observe 40 African Americans, which is less than our expected number, 48. In pool B, we observe 26 African Americans, which also below our expected value.
03

Determine which pool has smaller p-value

The p-value helps us to know how surprising or unlikely our observed data is under the assumption that the null hypothesis is true. Here, a smaller p-value indicates stronger evidence against the null hypothesis. Pool A has 40 African Americans (which is closer to our expected 48) and pool B has 26 (further from 48). Thus, Pool B would have a smaller p-value than Pool A: its observed number of African Americans is further from what we would expect if the null hypothesis were true.

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