2. Various studies done by Ms Makhalemele from SMU Chemistry department have shown the benefits of massage to manage pain. In one study, 125 adults suffering from osteoarthritis of the knees were randomly assigned to one of five 8-week regimens. The primary outcome was the change in the TUT and University of Pretoria Arthritis Index. This index is used extensively to assess pain and functioning in those suffering from arthritis. Negative values indicate improvement The following table summarizes the results of those completing the study. in Treatment 30 minute massage 1x per week 30 minute massage 2x per week 60 minute massage 1x per week 60 minute massage 2x per week Usual care, no massage 22 24 24 25 24 -17.4 -18.4 24.0 -24.0 -6.3 17.9 20.7 18.4 19.8 14.6 (8) Determine the pooled standard deviation

Individual actions can play a large role in the overall health of our planet. A researcher interested in evaluating environment friendly behaviors evaluated how often people recycle (per month) based on whether they have an overall optimistic or an overall pessimistic attitude toward eco-friendly behaviors. The results from this hypothetical study are given in the table.  Test whether or not recycling behaviors differed between groups using a .05 level of significance. State the value of the test statistics and the decision to retain or reject the null hypothesis. Compute effect size using eta- squared (n^2). Pessimistic Optimistic 3 4 0 9 4 6 2 8 1 9 6 5 3 6 5 8 0 6 5 7

Denny studied factors affecting cardiovascular reactivity to a postural change in a sample of healthy men and women. Change in systolic blood pressure (SBP) from supine to standing position was used as the measure of cardiac reactivity in a sample of 842 adults. Supine measurement of blood pressure was taken after participants had lain on an examination table for 15 minutes. Blood pressure was determined every 30 seconds using a Dinamap device for 2 minutes, and the measurements were averaged. Participants then stood up immediately, and additional measurements were made for another 2 minutes. Below is a table describing the characteristics of Denny’s sample: Which measures of dispersion, if any, are presented in this table (Ranges, SDs)? If age is normally distributed, approximately what percent of the sample would be younger than 50? If BMI is normally distributed, approximately what percent of the sample would have a BMI higher than 33.1?

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2. Recovering from surgery: A new postsurgical treatment was compared with a stan- dard treatment. Seven subjects received the new treatment, while seven others (the controls) received the standard treatment. The recovery times, in days, are given below. Can you conclude that the mean recovery time for those receiving the new treatment is less than the mean for those receiving the standard treatment? Use the a = 0.05 level. Treatment: Control: H₁: 12 18 (a) List the null and alternate hypetheses. Ho : (c) List the P-value. 13 23 (d) Make the comparison. 15 24 19 30 20 32 (b) List the distribution, the test statistic, the calculator program, and all input and output variables. 21 35 We reject Ho / We do not reject Ho (circle one) (e) State the final conclusion in the wording of the problem. 24 39

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5. An ecologist is studying the flower Iris versicolor. He measures the width and length of 100 petals of this flower from a large collection of specimens and obtains the following data. Width: AVG = 1.3 cm, SD = 0.2 cm Length: AVG = 4.3 cm, SD = 0.5 cm r = 0.65 One of the petals is at the 30th percentile of both width and length. Relative to all the petals at the 30th percentile width, this petal's length is (circle one) smaller than average about average larger than average Justify your answer using a written explanation and/or a diagram.