File 20% D Fri 9:22 PM a0E C www.weba the first eight years of the study, 1.5% o

Question

File 20% D Fri 9:22 PM a0E C www.weba the first eight years of the study, 1.5% of the 451 members of the Plus Fitness Association died. We are interested in the proportion of people over 50 who ran and died in the same eight-year period. NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Part (a) O X is the number of all runners that die, and P is the proportion of all runners that die O X is the proportion of all runners that die, and P is the number of all nunners that de. Xisthe proportion or people who ran and died ine egh-year period, and Pis the number of people who ran and died in the eight-year period. O X is the number of people who ran and died in the eight-year period, and P is the proportion of people who ran and died in the eight-year period Part (b) Which distribution should you use for this problem? (Round your answers to four decimal places.) O The standard The Student's -distribution shouid be used because V npa s 10, which implies a small sample.

Explanation / Answer

Here part (a) is correct

Part(b) It is a normal distribution with

Mean proportion p = 0.015

SE(p) = sqrt(0.015 * (1 - 0.015)/451) = 0.0057

Here confidence interval = 97%

alpha/2 = (1 - 0.97)/2 = 0.015

and the other alpha/2 = 0.015

Here confidence interval = p^ +- Z97% sqrt (p^ * (1-p^/n)

= 0.015 +- 2.17 * sqrt (0.015 * 0.985/451)

= 0.015 +- 0.0124

= (0.0026, 0.0274)

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