EDPSY 490A, Winter 2022 Homework 6 Chapter 6 (Part II) & Chapter 7 (20 pts) Due Feb 22 4:30pm Name: CHAPTER 6, PART II: APPROXIMATING POWER Homework Question 1 Imagine that you are writing a grant proposal in which you plan to give a particular math intervention to n=20 elementary students for one week (students are randomly selected from several schools in Seattle). At the end of the intervention week, you plan to measure your sample's math ability with a particular test that has a population mean of 100 (1402100) and a population variance of 80 (62:80). You believe that test scores of all students who receive this intervention (a treated population) will be distributed with a population mean of 104 (p. Alternavgzlo4). (The variance is assumed to be the same.) 3.) Assuming your belief that treated population mean is 104 is true, sketch a picture of what these two distributions look like (the null and the alternative) using 012.05 (2tailed). This will be a picture of two sampling distributions that overlap. Use the steps discussed in class: (i) draw the null, (ii) label the critical regions, (iii) draw the alternative, and (iv) nd the area of the alternative that lies in the critical region of the null and shade it in. USE PENCIL(S)! b) Examine your sketch in part #a. i. What is your approximate power (this is the shaded area)? ii. What is your approximate Type 11 error rate? iii. What is your Type I error rate? c) Imagine you changed your sample size to n=80. Resketch the null and alternative to reect the new sample size. d) Examine your sketch in part #c. i. What is your approximate power now (this is the shaded area)? ii. What is your approximate Type II error rate now? iii. What is your Type I error rate now? EdPsy490 Winter 22 HWG, p. 1 EDPSY 490A, Winter 2022 Homework 6 Chapter 6 (Part II) & Chapter 7 (20 pts) Due Feb 22 4:30pm Name: Homework Question 1, continued e) Imagine you decided to change your alpha level to a more stringent level to 1% instead of 5%. This requires a critical value that is larger than i196 (look in the text's Ztable). Using your sample size of n=80 from the last problem, resketch the null and alternative distributions to reect the new alpha level. f) Examine your sketch in part #e. i. What is your approximate power now (this is the shaded area)? ii. What is your approximate Type II error rate now? iii. What is your Type I error rate now? g) Examine how your answer changed from #b to #d. In general, when we increase our sample size, what happens to: i. power (increase, decrease, or no change)? ii. Type II error rate (increase, decrease, or no change)? iii. Type I error rate (increase, decrease, or no change)? h) Examine how your answer changed from #d to #f. In general, when we decrease our alpha level, what happens to: i. power (increase, decrease, or no change)? ii. Type II error rate (increase, decrease, or no change)? iii. Type I error rate (increase, decrease, or no change)? EdPsy490 Winter 22 HWG, p. 2