Question

The article “Statistical Evidence of Discimination” (J. Amer. Stat. Assoc., 1982: 773- 783) discusses the court case Swain v. Alabama (1965), in which it was alleged that there was discrimination against blacks in grand jury selection. Census data suggested that 25% of those eligible for grand jury service were black, yet a random sample of 1050 called to appear for possible duty yielded only 177 blacks. Using a level 0.01 test, does this data argue strongly for a conclusion of discrimination?

Answer 1

H₀: p=0.25 - null hypothesis

H_a: p≠0.25 - alternative hypothesis

z=(P_h-p)/$\sqrt{px(1-p)}/n$ =$(177/1050-0.25)/\sqrt{0.25x0.75}/1050=-6.09$

two-tail test given $\sigma$ =0.01 critival value z(0.005)=-2.58 or 2.58

rejection regions are if z<-2.58 or z>2.58 - we reject null hypothesis

z=-6.09 is less than -2.58 - reject null hypothesis

so this data argue strongly for a conclusion of discrimination