29.The Case of the Vanishing Women From 1966 to 1968, Dr. Benjamin Spock was tried for conspiracy to violate the Selective Service Act by encouraging resistance to the Vietnam War. By a series of three selections, no women ended up being on the jury. In 1969, Hans Zeisel wrote an article in The University of Chicago Law Review using statistics and hypothesis testing to argue that the jury selection was biased against Dr. Spock. Zeisel argues that, since Dr. Spock was a well-known pediatrician and author and millions of women had read his books, the court purposely kept women off of the jury and prejudiced the verdict. Although misdeeds occurred at all three stages of the jury selection process, this question only focuses on the first stage. In this stage, the clerk of the Federal District Court selected 350 people "at random" from the Boston City Directory. The directory contained several hundred names, 53% of whom were women. However, only 102 of the 350 people selected were women. a. Test the claim that 53% of the people listed in the directory were women. On the spreadsheet, use n 350, p 0.53, p^ = 0.2914, and a = 0.01. Should you reject this claim (you don't have to write out the entire solution; just use the spreadsheet to get the decision)? b. Since 53% is really, truly the proportion of women in the directory, what type of error (Type I or Type II) was made? Explain. C. If you reject a true claim with a level of significance that is virtually zero, what can you infer about the randomness of your sampling process?