# Dr. Spock's Problems

1. Estimation of proportions
2. Law

In 1969, the well-known pediatrician Dr. Benjamin Spock came to trial before a judge named Ford in Boston's Federal court house. He was charged with conspiracy to violate the Military Service Act (in addition to his work on child development he was active in anti-war protests in the 60s). A lawyer writing about the case that same year in the Chicago Law Review said about the case, "Of all defendants at such trials, Dr. Spock, who had given wise and welcome advice on child-bearing to millions of mothers, would haved liked women on his jury."

The jury was drawn from a panel of 350 persons, called a venire, selected by Judge Ford's clerk. This venire included only 102 women, even though 53% of the eligible jurors in the district were female. At the next stage in selecting the jury to hear the case, Judge Ford chose 100 potential jurors out of these 350 people. His choices included only 9 women.

If 350 people are chosen from all the eligible jurors in the district, how likely is it that the sample will include 102 women or fewer?

If 100 people are chosen at random without replacement from a group of people consisting of 102 women and 248 men, what is the chance that the sample will include 9 women or fewer? (Hint: remember the correction factor, if relevant.)

What do you conclude about the impartiality of Judge Ford's selection process?

Explain briefly.

George Michailides
gmichail@stat.ucla.edu