Stat2Lab19

(c) Use the normal approximation to find the chance that the average of the draws is less than 36.5. (d) Will the approximation in part (c) be a good approximation to the probability histogram for the average of the draws? Circle YES or NO and justify your answer: 3. Imagine you have been hired to analyze the data from a research study in which participants were drawn from undergraduate psychology courses. (For the purposes of this problem, you may assume that the participants represent a simple random sample from the population of all students in undergraduate psychology courses, although that is often not the case.) In the study, participants were given the Beck Depression Inventory (BDI), a 21-item measure of depressive symptoms with scores ranging from 0 to 63. Among the 120 study participants, the average score was 10 points; the standard deviation was also 10 points. (a) To make a confidence interval, you need a box model. Are the AVG and SD of this box known or estimated? ___________________ (b) Compute a 95%-confidence interval for the average BDI score of all students in undergraduate psychology courses. ~ avg < 36 5 36 5 - 35 -- 2 EV = 35 0 . 75 SE : 0 . 75 area = 95 45 95 45/2 = 47 775 - 50 + 47 725 : 97 725 merl ⊥ 97 725 % chance ↓ 35 36 5 ~ yes , because we know the sample size (400) is large enough , so the probability histogram would appear like a normal model W estimated (when pop is unknown W EV : 10 SE : # = 0 9129 & for 95 % : 1 . 95 10 I 1 . 95 (0 . 9129) = 10 I 1 . 7802 = (8 2198 , 11 . 7802)