Researchers were interested in comparing regular-intensity 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. Each exercise program lasted for eight weeks. The patients were followed for a total of 1.5 years. The researchers observed that 6 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. Data from this study should not be analyzed using a large-sample hypothesis test for a difference in two population proportions because the exercise program lasted more than 5 weeks. OData from this study should not be analyzed using a large-sample hypothesis test for a difference in two population proportions because the data came from a controlled experiment. Data from this study should not be analyzed using a large-sample hypothesis test for a difference in two population proportions because the number of deaths in each group are both greater than 10. Data from this study should not be analyzed using a large-sample hypothesis test for a difference in two population proportions because the number of deaths in each group are both less than 10. Data from this study should not be analyzed using a large-sample hypothesis test for a difference in two population proportions because the exercise program only lasted less than 10 weeks. (c) Use the Shiny app "Bootstrap Confidence Interval for Difference in Two Proportions" with a minimum of 1,000 samples 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. (Use Phigh Pregular Round your answers to three decimal places.) 0.667 x 0133 1x ) Interpret the interval in the context of the research. We are 95% confident that the true difference in the population proportions of patients who die within 1.5 years for the two exercise programs falls within this interval. O There is a 95% chance that the true mean proportion of patients in the high-intensity group who die within 1.5 years falls directly in the middle of this interval. O There is a 95% chance that the true difference in the population proportions of patients who die within 1.5 years for the two exercise programs falls directly in the middle of this interval. O We are 95% confident that the true mean proportion of patients in the regular-intensity group who die within 1.5 years falls within this interval, We are 95% confident that the true mean proportion of patients in the high-intensity group who die within 1.5 years falls within this interval