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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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Most popular questions from this chapter

California's controversial "three-strikes law" requires judges to sentence anyone convicted of three felony offenses to life in prison. Supporters say that this decreases crime both because it is a strong deterrent and because career criminals are removed from the streets. Opponents argue (among other things) that people serving life sentences have nothing to lose, so violence within the prison system increases. To test the opponents' claim, researchers examined data starting from the mid- 1990 s from the California Department of Corrections. "Three Strikes: Yes" means the person had committed three or more felony offenses and was probably serving a life sentence. "Three Strikes: No" means the person had committed no more than two offenses. "Misconduct" includes serious offenses (such as assaulting an officer) and minor offenses (such as not standing for a count). "No Misconduct" means the offender had not committed any offenses in prison. a. Compare the proportions of misconduct in these samples. Which proportion is higher, the proportion of misconduct for those who had three strikes or that for those who did not have three strikes? Explain. b. Treat this as though it were a random sample, and determine whether those with three strikes tend to have more offenses than those who do not. Use a \(0.05\) significance level. $$\begin{array}{|l|l|l|}\hline & \multicolumn{2}{c|} {\text { Three Strikes }} \\\\\hline & \text { Yes } & \text { No } \\ \hline \text { Misconduct } & 163 & 974 \\\\\hline \text { No Misconduct } & 571 & 2214 \\ \hline \text { Totals } & 734 & 3188 \\\\\hline\end{array}$$

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