Problem 4 (19 pts) A large class at a large mid-western University claims that the average student only needs to spend 6 hours on their weekly homework assignments with a SD = 4 hours. You believe the true class average is much higher, at least 8 hours with a SD : 4. To test their claim, you plan to randomly sample 25 students from the class of 2020 and ask them how many hours they spend on their homework per week. The null hypothesis is HD : p : 6 and the alternative is Ha : ,u > 6, with signicance level a : 0.05. a) You guess the true class average is pa : 8. What is the effect size? (1 pt) b) Which test should you use? And what is your critical value? (2 pts) c) Find the type I error, type II error and power. (4 pts) d) To let the power be at least 90%, what is the minimal sample size you need to have, given an : 8? (2 pm) e) Now you believe the true class average is pa : 10. Find the type I error, type II error and power for this value, using the sample size you get from part (d)? {4 pts) f) If a : 10 instead of 4, will the power for (e) decrease or increase given all other parameters unchanged? Please explain your result without any calculation. (2 pts) g) If a = 0.01 instead of 0.05, will the power for (e) decrease or increase given all other parameters unchanged? What about the type I error and type II error? Please explain your result without any calculation. (4 pts)