Question

2. Swain v. Alabama (1965) a lawsuit that argued that there was discrimination against African-Americans in grand jury selection. This case used a statistical argument based on the data that 181 African-Americans out of a random sample of 1075 were called to appear for possible duty.   Using the information that Census data show that 24% of those eligible for jury service were African-America conduct the hypothesis test to test the claim of discrimination. Use a significance level of 0.025.

1. State the null and alternative hypothesis
2. Compute the test statistic and the p-value.
3. Write your conclusion as if you are the expert witness in this case and explain what this p-value means to a jury.
4. What assumptions do we need in order for the conditions of the hypothesis test procedure to be met?

Answer 1

a)
Below are the null and alternative Hypothesis,
Null Hypothesis: p = 0.24
Alternative Hypothesis: p < 0.24

b)
Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.1684 - 0.24)/sqrt(0.24*(1-0.24)/1075)
z = -5.5

P-value Approach
P-value = 0.0000

c)
As P-value < 0.025, reject the null hypothesis.
P-value indicates the probabiliity of occurrence of pcap<0.1684 if p = 0.24
As this probability is very small, we reject the null hypothesis

d)
Data is normally distributed and
np >= 5 and n(1-p) >=5