1 THE UNIVERSITY OF WESTERN ONTARIO LONDON CANADA Department of Psychology Intersession 1. Psychology 281 Third Exam Medical researchers sometimes use a digital sonomicrometer to measure the blood vessel diameters of cardiac patients before and after treatment. In one study, it is predicted that the diameter of patients' blood vessels will decrease by more than 400 micrometers following treatment with an experimental drug. To test this hypothesis, the blood vessel diameters (measured in micrometers) of 8 cardiac patients are compared before and 1 week after administration of the drug, yielding the following data: Patient IDs 019M 328M 114F 985M 167F 033F 664M 230F Blood Vessel Diameters Before Treatment After Treatment 7850 6448 4023 8137 5775 5890 6704 7852 6015 4124 4157 6309 5775 4362 6832 5396 a) Perform whichever statistical procedure(s) is/are required to test the researchers' hypothesis (α .05). [10 points] b) In addition to the average size of the blood vessels of cardiac patients, the variance of their blood vessel diameters may also be significantly different from that of the general (non-patient) population, which (in micrometers) is known to be 2,000,000. Perform the appropriate statistical test(s) to see whether the variance of the 8 patients' beforetreatment blood vessels (from part 'a') differs significantly from the general population value (α .05). [8 points] 2. Two new therapies designed to increase levels of self-esteem are tested in a clinical population. Nine subjects are randomly assigned to a control group (C) which is exposed to a placebo procedure. We also randomly assign 7 subjects to Therapy A (TA) and 9 other subjects to Therapy B (TB). Self esteem scores are measured for each group after a 2-month period and the following results are obtained (no subjects dropped out of the experiment): 2 Group C: Group TA: Group TB: X = 11.111 X = 14.429 X = 18.667 S = 2.848 S = 3.599 S = 2.872 a) Determine whether there is an overall significant treatment effect (α .05). (12 points) b) Assuming you found a significant treatment effect in part 'a' (even if you didn't), perform post hoc analyses to determine which particular pairs of groups differ significantly. Assign an alpha of .05 to each comparison that you make (10 points) 3. A particular Intersession stats prof is noted for 2 things: the number of pages of notes his students have to write down each night and the number of pieces of chalk he destroys each night. To see if there is any relationship between these, a record is kept of the number of pages of notes his students write during 6 different lectures in June and the number of pieces of chalk the prof destroys on these nights. The following data were obtained: Night # Note Pages Monday Tuesday Wednesday Monday Tuesday Wednesday 8 4 12 6 9 7 # Chalks Destroyed 5 1 7 4 8 2 a) Is there a significant positive correlation between # of note pages and # of pieces of chalk destroyed (α .05)? [10 points] b) How many pieces of chalk would the prof be predicted to destroy on a night that his students write down 10 pages of notes, and what are the 95% bounds to the error of this prediction? [10 points] 4. An educational psychologist is studying two different approaches to teaching 1st graders basic concepts of arithmetic. She randomly assigns children to one of two different groups which will be exposed to one or the other teaching-approaches and obtains the children’s scores (out of 100) on an arithmetic test before and after 10 weeks of instruction. She then tests to see whether there is a significant difference between the two approaches in the amount by which the children’s scores change. Using the following data, perform the appropriate analyses to address the educational psychologist’s research question (α = .05). Teaching Approach One Teaching Approach Two 3 Scores Before 60 54 77 86 71 5. Scores After 63 58 80 86 74 Scores Before 55 76 65 54 67 Scores After 75 79 80 54 87 According to genetic theory, when tall yellow begonias are crossed with short red begonias they should produce 4 types of offspring in a 9:3:3:1 ratio, representing tall red, tall yellow, short red, and short yellow flowers, respectively. A botanist tests the theory by collecting the following data: the number of begonias of each type that resulted from a tall yellow/short red crossing. Tall red Tall yellow 172 55 Short red 72 Short yellow 16 a) Do these data conform to the theory (α .05)? [10 points] b) The botanist has also created a non-toxic chemical fertilizer which she believes will change the height and colour characteristics of begonias. She again crossbreeds tall yellow begonias with short red begonias and sprays the offspring of these flowers daily with the chemical fertilizer. She collects the following frequency data after spraying: Tall red Tall yellow Short red Short yellow 100 40 45 9 Based on the two data sets from parts 'a' and 'b', does it appear that the height and colour characteristics of begonias can be significantly altered by the fertilizer (α .05)? [12 points] 6. The stress of taking an important exam has been suspected of influencing students' quality of sleep. To test this hypothesis, we measure sleep quality (number of hours of deep sleep per night) in a group of six undergraduates 1 month prior to an exam (baseline), the night before an important exam (NB), and the night after the exam (NA). We obtain the following information: Baseline Ti 21.0 ΣX2 = 227.22, and SSSubjects = 2.837 NB NA 18.0 24.0 4 a) Is there a significant difference in sleep quality between the three measurement periods (α .01)? [12 points] b) Prior to data collection it had been predicted that sleep quality at the baseline and NA measurement periods would not differ significantly. Is this prediction supported by the data, using α .05? [6 points] Answers 1. a) t = 2.061: reject Ho, the hypothesis/prediction is supported; b) χ2 = 6.675: do not reject Ho, the variance does not differ significantly from 2,000,000 2. a) F = 13.61: reject Ho, a significant treatment effect exists; b) Q’s = 3.96, 3.10, and 7.06: all reject Ho so all comparisons are significant 3. a) r = .829, t = 2.965: reject Ho, a significant positive correlation exists; b) 6.434 ± 5.453 4. (i) F = 39.26: reject Ho, the variances differ significantly so now do a Wilcoxon test; (ii) T = 22 (or 33): do not reject Ho, there is no evidence for any significant difference between the two approaches 5. a) χ2 = 3,96: do not reject Ho, the theory is supported; b) χ2 = .905: do not reject Ho, the fertilizer has no effect 6. a) F = 16.988: reject Ho, a significant difference exists; b) t = 2.914: reject Ho, the prediction is not supported.