A school psychologist was interested in the effect of a program designed to reduce adjustment problems in newly-transferred students. From her years of working at the school, she knew that the average score on a scale of adjustment difficulties for transfer students was 58 with a standard deviation of 10. After the program began, she tested 50 students and found their mean to be 52. a. Define the populations. b. What is the psychologist's research hypothesis (in words and symbols)? c. What is the psychologist's null hypothesis (in words and symbols)? d. What type of distribution is the comparison distribution? e. What are the three characteristics (i.e., shape, mean, and standard deviation) of the comparison distribution? How do you know what shape it has? f. What is the Z score cut-off on the comparison distribution? (Use the .01 significance level.) g. What is the sample's Z score on the comparison distribution? h. Sketch the comparison distribution. (Be sure to label the horizontal axis of the distribution using Z and raw scores, shade the region of rejection of the null hypothesis, label the cutoff Z score(s), and label the sample's Z score). i. With regard to the hypotheses in this study, what decisions should the psychologist make? j. What is the independent variable in this study? k. What is the dependent variable in this study? l. With regard to the variables in this study, what should the psychologist conclude? m. Figure the effect size. By conventional standards, how big is the effect? n. Figure the 99% confidence interval. o. In terms of this study, what does the confidence interval tell the psychologist? p. Sketch the experimental distribution. (Be sure to label the horizontal axis of the distribution using Z and raw scores, and indicate the Z scores and X scores at the lower and upper limits of the 99% confidence interval). q. Explain how the psychologist could use the confidence interval to make decisions about the hypotheses in (i.)