Hypothesis Testing

Question 1

In a famous 1968 trial, U.S. pediatrician and anti-war activist Dr. Benjamin Spock was accused of conspiracy to violate the Selective Service Act, the mechanism by which Americans were drafted to fight in the Vietnam War. Spock's defence lawyers challenged jury selection procedure, on the grounds that none of the 12 jurors were women. (Women were perceived as being more favourably disposed towards Spock.) Suppose that 50% of eligible jurors are women, and that jurors are chosen at random. What is the probability of an all male jury occurring purely by chance? What does this tell us about the hypothesis that selection of Spock's jury was random? Give a detailed statistical argument.

Question 2

Suppose John took Compling2 in Spring 2004 and Mary took it in Spring 2005. John's homework grades were 100, 98, 87, 92, and 93, and Mary's were 83, 92, 87, 92, 91, and 93. John claims that his homework grades show he's a better student than Mary, but Mary says she can give a detailed statistical argument against his claim. Give such an argument. (For purposes of this assignment, you should assume that professors and graders are perfect. You can assume that any time you like, actually. :->)

Question 3

John grudgingly acknowledges that Mary is right, but he says he had a cold the week that the third assignment was due, and did not do as well as he should have. He says that if he'd gotten a higher score on that one homework, he could give Mary a detailed statistical argument that he's a better student. Is he right? How much better would he have to have done in order to convince her, assuming she's a conventional sort of person? What if she's the sort of person who wants to be 99% confident in things?