1 Select all that apply. 10 points A Canadian study measuring depression level in teens (as reported in theJournal of Adolescence, vol. 25, 2002) randomly sampled 112 male teens and 101 female teens, and scored them on a common depression scale (higher score representing more depression). The researchers suspected that the mean depression score for male teens is higher than for female teens, and wanted to check whether data would support this hypothesis. If 1 and 2 represent the mean depression score for male teens and female teens respectively, which of the following is an appropriate pair of hypotheses in this case? Check all that apply. 1. H0: 1 - 2 = 0 Ha: 1 - 2 < 0 2. H0: 1 - 2 > 0 Ha: 1 - 2 = 0 3. H0: 1 = 2 Ha: 1 > 2 4. H0: 1 - 2 = 0 Ha: 1 - 2 > 0 Question 2 Select one answer. 10 points A study measuring fitness level in teens randomly sampled 112 male teens and 101 female teens with a higher score indicating more fitness. Researchers suspected that the fitness level for male teens (1) is higher than for female teens (2), and wanted to check whether the data would supported this hypothesis. The following hypotheses were tested: H0: 1 = 2 Ha: 1 < 2 Sample N Mean SD 1(M) 112 7.38 6.95 2(F) 10 2 7.15 6.31 t-test of difference: df = 210 t-value = 0.25 p-value = 0.400 Which of the following is an appropriate conclusion based on the output? 1. The data do not provide sufficient evidence to conclude that the mean fitness score of male teens is higher than that of female teens. 2. The data do not provide sufficient evidence to reject H0, so we accept it, and conclude that female and male teens do not differ in mean fitness score. 3. The data provide sufficient evidence to conclude that male and female teens do not differ in mean fitness score. 4. The data provide sufficient evidence to reject H0 and to conclude that the mean fitness score for male teens is higher than that of female teens. Question 3 Select one answer. 10 points As first year residential students get familiar with campus life, some students spend less time speaking with the residential advisor. Suppose individual call time (in minutes) is measured in September and then later in December. The results are as shown: Studen t Average Weekly Call (Sept) Average Weekly Call (Dec) 1 45 38 2 47 45 3 48 48 4 38 33 5 48 39 We wish to test whether there is a statistically significant decrease in individual call time. Given the design of the study and the question of interest, which one of the following statistics test is relevant to use? 1. Paired t-test and CI: Sept; Dec 2. Two-sample t-test and CI: Sept; Dec Question 4 Select one answer. 10 points To determine the relative effectiveness of different study strategies for the SAT, suppose three groups of students are randomly selected: One group took the SAT without any prior studying; the second group took the SAT after studying on their own from a common study booklet available in the bookstore; and the third group took the SAT after completing a paid summer study session from a private test-prep company. The means and standard deviations of the resulting SAT scores from this hypothetical study are summarized below: Since we are comparing more than 2 groups, we will use ANOVA to test whether the data provide evidence that SAT score is related to study strategy. One of the conditions that allows us to use ANOVA safely is that of equal (population) standard deviations. Can we assume that this condition is met in this case? 1. 2. No, since the three sample standard deviations are not all equal. No, since the population standard deviations are not given, so we cannot check this condition. 3. Yes, since 5.7 4.9 < 2. 4. Yes, since 5.7/4.9 < 2. Question 5 Select all that apply. 10 points To determine the relative effectiveness of different study strategies for the SAT, suppose three groups of students are randomly selected: One group took the SAT without any prior studying; the second group took the SAT after studying on their own from a common study booklet available in the bookstore; and the third group took the SAT after completing a paid summer study session from a private test-prep company. The means and standard deviations of the resulting SAT scores from this hypothetical study are summarized below: Since we are comparing more than 2 groups, we will use ANOVA to test whether the data provide evidence that SAT score is related to study strategy. The following hypotheses were tested: H0: 1 = 2 = 3 Ha: 1, 2, and 3 are not all equal The analysis was run on the data and the following output was obtained: Which of the following is a valid conclusion based on the output? Check all that apply. 1. The data provide strong evidence that SAT scores are related to learning strategy. 2. The data provide strong evidence that SAT scores are related to learning strategy in the following way: The mean SAT score for students who pay for coaching is higher than the mean SAT score for students who study themselves, which in turn is higher than that of students who do not study for the test. 3. The data provide strong evidence that the three mean SAT scores (representing the three learning strategies) are not all equal. 4. The data do not provide sufficient evidence that SAT scores are related to learning strategy. Question 6 Select one answer. 10 points A GRE course prep company advertises that its course can significantly raise students' GRE Verbal Reasoning scores. In order to assess the accuracy of this claim, a researcher randomly selected two independent samples of 30 graduating seniors from a local university, who were applying to business school. One group of 30 students took the GRE, without any preparation. The other group of 30 students took the GRE after completing a GRE prep course. The researcher then compared the performance for the two groups to determine whether there was difference on the GRE Verbal Reasoning scores from group without any preparation and the group completing the GRE prep course. What hypothesis testing technique should the researcher use to analyze the data? ANOVA Paired t-test z-test for the population mean Two-sample t-test Question 7 Select one answer. 10 points In a hypothetical study, a pharmaceutical company is interested in finding the dosage of a new medication that best treats panic attacks. Ninety people, who are diagnosed with panic attacks, were randomly assigned to three groups: (1) 20 milligrams of the new drug, (2) 30 milligrams of the new drug, and (3) 40 milligrams of the new drug. After 30 days on the medication, each participant records the number of panic attacks they have experienced in the previous seven days. What hypothesis testing technique should the researcher use to analyze the data? Two-sample t-test z-test for the population mean ANOVA Paired t-test