1} A researcher would like to examine how the chemical tryptophan, contained in foods such as turkey, can affect mental alertness. A sample of n = 9 college students is obtained and each student's performance on a familiar video game is measured before and after eating a traditional Thanksgiving dinner including roast turkey. The average score dropped by M = 14 points after the meal with 55 = 1152 for the difference scores. a. Is there is significant difference in performance before eating versus after eating? Conduct a hypothesis test to answer this question. b. Interpret the results of the hypothesis test. c. Compute Cohen's d. What does it say about the size of the effect? d. Compute r2. What does it say about the size of the effect? e. Compute the 95% confidence interval. What does the confidence interval mean? 2) A researcher is interested in a drug to treat depression. A sample of n = 16 individuals is selected from a population with p. = 30 on a self-reported measure of happiness. After the drug is administered to the individuals, the sample mean is found to be M = 33 and the sample variance is found to be 52 = 64. a. Is there is significant difference between the population and the sample on self-reported happiness? Conduct a hypothesis test to answer this question. b. Interpret the results of the hypothesis test. c. Compute Cohen's d. What does it say about the size of the effect? d. Compute r2. What does it say about the size of the effect? e. Compute the 95% confidence interval. What does the confidence interval mean? 3) An educational psychologist hypothesizes that frequent testing will increase retention of class material. In one section of an introductory course, students are given quizzes each week. A second section of the same course receives only two tests during the semester. At the end of the semester, both sections receive the same final exam, and the scores are summarized below. Freguent Quizzes Two Exams n=20 n=20 M=73 M=68 55:722 55:798 a. Is there is significant difference between the classes on the final exam? Conduct a hypothesis test to answer this question. b. Interpret the results of the hypothesis test. c. Compute Cohen's d. What does it say about the size of the effect? d. Compute r2. What does it say about the size of the effect? e. Compute the 95% confidence interval. What does the confidence interval mean