EXCEL MINITAB TI-84 PLUS The Case of the Vanishing Women TECHNOLOGY Technology 413 Extended solutions are given in the technology manuals that accompany this text. Technical instruction is provided for Minitab, Excel, and the TI-84 Plus. 53% 29% 9% 0% From 1966 to 1968, Dr. Benjamin Spock and others were 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. Dr. Spock was a well-known pediatrician and author of books about raising children. Millions of mothers had read his books and followed his advice. The jury selection process for Dr. Spock’s trial, shown at the right, can be used to explore the possibility that the jury selection was biased. Stage 1. 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. Stage 2. The trial judge, Judge Ford, selected 100 people “at random” from the 350 people. This group was called a venire and it contained only nine women. Stage 3. The court clerk assigned numbers to the members of the venire and, one by one, they were interrogated by the attorneys for the prosecution and defense until 12 members of the jury were chosen. At this stage, only one potential female juror was questioned, and she was eliminated by the prosecutor under his quota of peremptory challenges (for which he did not have to give a reason). 1. The Minitab display below shows a hypothesis test for a claim that the proportion of women in the city directory is p = 0.53. In the test, n = 350 and np ≈ 0.291. Should you reject the claim? What is the level of significance? Explain. 2. In Exercise 1, you rejected the claim that p = 0.53. But this claim was true. What type of error is this? 3. When 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? 4. Describe a hypothesis test for Judge Ford’s “random” selection of the venire. Use a claim of p = 102 350 ≈ 0.291. (a) Write the null and alternative hypotheses. (b) Use technology to perform the test. (c) Make a decision. (d) Interpret the decision in the context of the original claim. Could Judge Ford’s selection of 100 venire members have been random? EXERCISES MINITAB Test and CI for One Proportion N Event Sample p 99% CI for p Z-Value P-Value 350 102 0.291429 (0.228862, 0.353995) -8.94 0.000 p: event proportion Null hypothesis H0: p = 0.53 Normal approximation used Alternative hypothesis H1: p ≠ 0.53
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