A university conducted a study of whether running is healthy for men and women o

Question

A university conducted a study of whether running is healthy for men and women over age so. During the first eight years of the study, 1.8% of the 456 members of a fitness association died. we are interested in the proportion of people over 50 who ran and died in the same eight-year period NOTE: I 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. O Part (a) Defire the Random Variables Xand P, in words. X is the number of people who ran and died in the eght-year period, and P' is the proportion of people who ran and died in the eight-year period OX is the proportion of all runners that die, and Pis the number of all runners that die O X is the proportion of people who ran and died in the eightyear period, and P is the number of people who ran and died in the eight year period O Part (b) Which distribution shouid you use for this problem? (Round your answers to four deoimal places Explain your choice The standand normal dstibution should be used because we are interested in proportions The Students fdistribution should be used because we do not know the standard deviation. The binomial distribution should be used because the two outcomes are "the runner died" and "the runner did not die O The Studenfs f-distribution should be used because vmp10, which implies a small sample.

Explanation / Answer

Ans:

a)X is the number of people who ran and died in the 8 year period and p is thr proportion of the people who ran and died in the eight year period.(First option is correct)

b)propotion will follow normal distribution with

mean=0.0180

standard dev=sqrt(0.018*(1-0.018)/456)=0.0062

(first option is correct)

c)z value for 97% CI is 2.17

97% CI

=0.018+/-2.17*sqrt(0.018*(1-0.018)/456)

=0.0180+/-0.0135

=(0.0045,0.0315)

Margin of error=0.0135

d)We are 97% confident that the population proportion of runners over the age of 50 that will die in the next eight years is between the interval values.

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