The population of interest is all eligible jurors, with 53% of them being women. The null hypothesis is that Judge Ford is gender neutral, while the alternative is that he is biased against women. From the population of interest (where the number of people is big) a simple random sample (SRS) (under the null hypothesis) of n=350 persons is drawn by Judge Ford's clerk, which comprises the observed venire. The estimated proportion of women in the sample is 102/350=.291 or about 29%. The expected proportion of women in the sample is p=53%, with a standard error given by SE(estimated p)=square-root(p(1-p)/n)= square-root(.53*.47/350)=2.7%. The long run histogram of the estimated proportion if the null hypothesis is true is normal, centered at 53% with variance equal to .027^2. We calculate the z-score and get a value of (29-53)/2.7=-8.9%, with an associated P-value about 0%. Therefore, it is highly unlikely that 102 or fewer women would be selected in a venire of 350 persons by chance.

The population of interest is the observed venire. The null and the alternative hypotheses remain the same. From this population a SRS (under the null) of 100 persons is selected by Judge Ford. The proportion of women in the population is 29%, while the estimated proportion in the sample is 9%, with an associated standard error equal to .846*square-root(.29*.71/100)=3.8%. The number .846 is the finite population correction factor (square-root((350-100)/(100-1))=.846. The long run histogram of the estimated proportion if the null hypothesis is true is normal, centered at 29% with variance equal to .038^2. We calculate the z-score and get a value of (9-29)/3.8=-5.2, with an associated P-value about 0%. Therefore, it is highly unlikely that 9 or fewer women would be selected in a sample of 100 persons by chance.

There is strong evidence that Judge Ford discriminated against women in selecting Dr. Spock's jury.