For Questions 7-13, refer to the following information: Alexander (2014) studied the necessary critical thinking skills for public health practitioners compared to how critical thinking skills were taught in MPH programs. Let us suppose that 7 students were randomly selected from a population of MPH students to participate in a program to enhance critical thinking to prepare them for the skills needed to be successful MPH practitioners. Each student was given a critical thinking task prior to training and was re-evaluated after the training. Higher scores on the task indicated more critical thinking skills used, such as identifying and assessing issues, analyzing data relevant to the issue at hand, and reflecting on the results in order to address the issues. Before and after training scores for critical thinking are below, resulting in a mean difference of -3.69 and an Sa of 2.187. Assuming the results are normally distributed, test the claim that the program increased critical thinking skills using a 0.05 significance level. Participant 1 Before 2 3 4 5 6 7 3 2.1 4.3 5.2 5.5 6.0 2.7 After 7.4 6.5 8.1 10.0 9.1 5.0 8.5 7. What type of test should you use to test the null hypothesis? (1 point) a. Two sample t-test for variances assumed unequal b. Two-sample Z-test c. Paired t-test d. Two sample t-test for variances assumed equal 8. What is the null hypothesis? (1 point) a. u u > 0 b. u1 u c. ua 0 d. ua > 0 e. f. d 0 9. What is the alternative hypothesis? (1 point) - U2 > 0 a.u1 b. u u c. ua 0 d. ua < 0 e. d>0 f. d o 10. What is the critical value? (1 point) a. 1.645 b. 1.960 C. -1.943 d. -1.960 e. -1.645 11. What is the value of the test statistic? (1 point) a. -4.46 b. -4.30 C. 0.29 d. 9.08 12. What conclusion should you make regarding the null hypothesis? (1 point) a. Fail to reject the null hypothesis due to insufficient evidence and conclude that the critical thinking training did not increase critical thinking skills. b. Fail to reject the null hypothesis due to sufficient evidence and conclude that the critical thinking training did increase critical thinking skills. c. Reject the null hypothesis due to insufficient evidence and conclude that the critical thinking training did not increase critical thinking skills. d. Reject the null hypothesis due to sufficient evidence and conclude that the critical thinking training did increase critical thinking skills. 13. Two genetic variants, BRCA1 and BRCA2, are associated with increased risk of breast and ovarian cancer in women. According to the latest estimates by the National Cancer Institute, the incidence of breast cancer by age 70 is 0.635 among women with the BRCA1 variant. Among a group of 5 women identified as having the BRCA1 variant, what is the probability that exactly 2 women will be diagnosed with breast cancer? (2 points) a. 0.111 b. 0.138 c. 0.196 d. 0.400