A pharmaceutical company develops a new drug that helps obese patients who are not currently diabetic avoid contraction of diabetes. The conduct conducts a trial splitting a sample of 135 patients into two groups, a drug group and a placebo group. They then monitored the patients for 5 years and noted how many patients in each group contracted diabetes. The company wants to conduct a Chi-Squared test for Independence to assess whether their new drug has any effect on the contraction of diabetes amongst obese patients. Use this data to answer questions 1-6. Drug Placebo Number of Patients Contracted diabetes Did not contract diabetes 51 39 18 27 1. Calculate the percentage of patients who took the drug who contracted diabetes and the percentage of patients who took the placebo who contracted diabetes. Calculate the rate difference and rate ratio. Do you believe there is preliminary evidence to suggest there might be a difference in the rate of diabetes contraction between persons on the drug and persons taking the placebo? Why or why not? 2 2. Identify the correct critical value, ,df . 3. Calculate the test statistic, 2 test . 4. The company statistician tells you that the p-value of the test is 0.0678. Summarize the result of the study. Compare the proportion of patients who contracted diabetes in the drug group to the placebo group. Compare the test statistic to the critical value. Compare the p-value to alpha. Is there statistically significant evidence to suggest that the drug is effective in preventing the contraction of diabetes? Is there any other evidence to suggest that the drug is effective? Explain why or why not. An occupational therapist hypothesizes that there is a linear relationship between the number of years her patients spent in a desk job and the number of weeks it takes to complete therapy. The following table contains data from a sample of nine of her patients. Use this data to answer questions 7-13. Desk Job Yrs (j) Therapy Wks (t) A 29.9 12 B 20 8 J C D E F G H I 14.2 20.6 12.1 23.4 25.4 24.7 13.2 27.6 6 7 5 11 9 11 5 12 5. List the assumptions of conducting a simple linear regression, and at least one method to verify each of the assumptions you list. 6. Create a scatterplot of the data. Is the occupational therapist's hypothesis is valid? 2 2 7. Calculate the following summary statistics: j , t , s j , st , s jt 8. Calculate and interpret the pearson's correlation coefficient between the variables J and T, r jt , and the 2 coefficient of determination between the variables J and T, r jt . 9. Determine the coefficients of the least squares regression line for the following model between years in t =a+b j i+ i a desk job and weeks in therapy (equations on p.487): i 10. The therapist's statistician tells you that the mean squared error for this model is equal to 0.93783. Create and interpret a 95% confidence interval for the regression coefficient b. 11. Use the least-squares regression line to predict the expected number of weeks of therapy needed for a patient who has spent 22.5 years in a desk job