Stanford University conducted a study of whether running is healthy for men and women over age 50. During the first eight years of the study, 6.9% of the 591 members of the 50-Plus Fitness Association died. We are interested in the proportion of peOple over 50 who ran and died in the same eight-year period. a. Dene the random variables X and P' in words. X is the number of people over 50 who ran and died in the same eight-year period. P' is the 0 population proportion of people over 50 who ran and died in the same eight-year period from the sample of 591 members of the 50-Plus Fitness Association. X is the population proportion of people over 50 who ran and died in the same eight-year period \\- from the sample of 591 members of the 50-Plus Fitness Association. P' is the number of people over 50 who ran and died in the same eight-year period. X is the number of households in the survey where women make the majority of the purchasing decisions. P' is the population proportion of households where women make the majority of the purchasing decisions. X is the number of people over 50 who ran and died in the same eight-year period from the sample of 591 members of the 50-Plus Fitness Association. P' is the population proportion of people over 50 who ran and died in the same eight-year period. X is the number of people over 50 who ran and died in the same eight-year period. P' is the estimate of proportion of people over 50 who ran and died in the same eight-year period from the sample of 591 members of the 50-Plus Fitness Association. b. Which distribution should you use for this problem? Explain your choice. (0.069) (0.931) P' ~ N (0.069, 591 ) , since a normal distribution can be used to approximate a binomial distribution. 0.069 0.069 _\\ P' N N (0.069, \\/(5)g(1)) , since a normal distribution can be used to approximate a binomial distribution. (0.069) (0.931) I 7' P B(0.069, 591 ) , since a binomial distribution can be used to approximate a normal distribution. . P' ~B(41,0.069), since a binomial distribution can be used to approximate a normal distribution. (0.069) (0.931) I . P N(41, 591 ), since a normal distribution can be used to approximate a binomial distribution. c. Construct a 90% condence interval for the population proportion of people over 50 who ran and died in the same eight-year period. Enter your answer in interval notation. Round your answer to four decimal places. Do not round any intermediate calculations. (0.4464,0.5536) |j d. Explain what a "90% condence interval" means for this study. If we took repeated samples of people over 50 who ran over eight years, approximately 90% of the '- confidence intervals calulated from those samples would contain the sample proportion of people over 50 who ran and died in the same eight-year period. If we took repeated samples of people over 50 who ran over eight years, the sample proportion of people over 50 who ran and died in the same eight-year period would equal the population proportion in approximately 90% of the samples. If we took repeated samples of people over 50 who ran over eight years, approximately 90% of the o confidence intervals calulated from those samples would contain the true value of the population proportion of people over 50 who ran and died in the same eight-year period. \\ If we took repeated samples of people over 50 who ran over eight years, approximately 90% of the samples would produce the same confidence interval