Researchers were interested in comparing regularintensity exercise and high-intensity exercise for patients recovering from hospitalization due to chronic obstructive pulmonary disease (COPD). The researchers followed patients in Denmark who were enrolled in each of the two types of exercise programs (“Increased Mortality in Patients with Severe COPD Associated with High-Intensity Exercise: A Preliminary Cohort Study,” Journal of Chronic Obstructive Pulmonary Disease [2016]: 2329–2334). Each exercise program lasted for 8 weeks. The patients were followed for a total of 1.5 years. The researchers observed that 5 out of the 15 patients in the high-intensity group died within a year and a half, but that none of the 16 patients in the regular-intensity group died within a year and a half.

a. Explain why the data from this study should not be analyzed using a large-sample hypothesis test for a difference in two population proportions.

b. Carry out a hypothesis test to determine if there is convincing evidence of a difference in the population proportions who die within 1.5 years for the two exercise programs. Use the Shiny app “Randomization Test for Two Proportions” (in the collection at statistics .cengage.com/PSO6e/Apps.html) to report an approximate P-value and then use it to reach a decision in the hypothesis test. Remember to interpret the results of the test in context.

c. Use the Shiny app “Bootstrap Confidence Interval for Difference in Two Proportions” (in the collection at statistics.cengage.com /PSO6e/Apps.html) to obtain a 95% bootstrap confidence interval for the difference in the population proportions in patients who die within 1.5 years for the two exercise programs. Interpret the interval in the context of the research.