Question 2 15 pts A recent study looked at the relationship between condom use and the spread of AIDS, by following heterosexual couples in which one partner was infected with HIV. The couples were classied by their condom use. Of the 98 couples who always used condoms, 4 partners became infected with HIV. 0f the 67 couples who did not always use condoms, 11 partners became infected. Test whether the proportions of partners who became infected with HIV are different for each group, using a 5% level of signicance. Give each of the following to receive full credit: 1) the appropriate null and alternative hypotheses; 2) the appropriate test; 3) the decision rule; 4) the calculation of the test statistic; and 5) your conclusion including a comparison to alpha or the critical value. You M show your work to receive full credit. Partial credit is available. Question 1 15 pts Researchers are testing the effectiveness of a new smoking cessation program. At the close of the program the mean number of cigarettes smoked for the 328 people who completed the program was 4.3 with a standard deviation of 5.22. The mean number of cigarettes smoked per day for the 298 people who did not complete the program was 13 with a standard deviation of 8.97. Is there a difference between the two means? Use a 5% level of signicance to answer the question. Assume equal variances. Give each of the following to receive full credit: 1) the appropriate null and alternative hypotheses; 2) the appropriate test; 3) the decision rule; 4) the calculation of the test statistic; and 5) your conclusion including a comparison to alpha or the critical value. You MUST show your work to receive full credit. Partial credit is available. Question 3 15 pts In a recent study, fine motor skills were measured in a sample of kindergarteners before and after 7 months of occupational therapy. Higher scores indicate stronger fine motor skills. The data are presented below. Is there evidence of a change in fine motor skills? Use a 5% level of significance. Give each of the following to receive full credit: 1) the appropriate null and alternative hypotheses; 2) the appropriate test; 3) the decision rule; 4) the calculation of the test statistic; and 5) your conclusion including a comparison to alpha or the critical value. You MUST show your work to receive full credit. Partial credit is available. Pre Post 91 94 61 85 85 112 87 105 98 101 115 106 91 109 59 94 112 112Question 4 15 pts A recent survey asked adults about their beliefs about premarital sex and whether they thought birth control should be made available to teenagers. The data are below. Test whether beliefs about premarital sex and beliefs about birth control are independent using a 5% significance level. Give each of the following to receive full credit: 1) the appropriate null and alternative hypotheses; 2) the appropriate test; 3) the decision rule; 4) the calculation of the test statistic; and 5) your conclusion including a comparison to alpha or the critical value. You MUST show your work to receive full credit. Partial credit is available. Teenage Birth Control Premarital Sex Disagree Agree Total Always wrong 98 68 166 Sometimes 78 79 |157 Wrong Not wrong 138 237 375 Total 314 384 698