Technology Activity Using the TI-84+ CE and Unit 7 Knowledge Formative Assessment Things to Know before you start: Recall from 7.2, if a P-value < 0.01, then the null hypothesis will be rejected at the common levels of a = 0.01, 0.05, and 0.10. If P-value > 0.10, you would fail to reject the Ho for these common levels. The P-value gives you the lowest level of significance for which the sample statistic allows you to reject the null hypothesis. What is a Type 1 error? A Type II error? THE CASE OF THE VANISHING WOMEN 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 against Dr. Spock. 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. Zeisel argued that, by keeping women off the jury, the court prejudiced the verdict. The jury selection process for Dr. Spock's trial is shown at the right. EXERCISES 1. Use the calculator to conduct a hypothesis test for the percentage of women who are in the directory. (Stage 1). Should you reject the claim? What is the level of significance? Use your warm-up to help you. Explain your answer. 2. In Exercise 1, if you rejected the claim that Phis? 0.53, but the claim was true. What type of error is 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? 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). 4. Describe a hypothesis test for Judge Ford's "random" selection of the venire. Use a claim of Р 102 ≈ 0.2914. 350 (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? You may work with a partner, but must hand in your own work. When finished, hand in your calculator activity and complete the questions on the backside of this page. You will be offered a retake tomorrow (no index card). Your two test scores will be averaged together. You must complete ALL four questions and hand in WITH YOUR UNIT 7 PACKET tomorrow in order for your retake. REMEMBER... For Unit 8- Unit 10, ALL assignments must be completed in order to use an index card on your exam.