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following cardiac surgery, patients are encouraged to exercise regularly (assume

ID: 3133500 • Letter: F

Question

following cardiac surgery, patients are encouraged to exercise regularly (assume that regular exercise is defined as exercising on 3 or more days per week). A physician suspects that the patients exercise regularly immediately following cardiac surgery but tend to reduce, even stop exercising completely, over time. An investigation is planned to estimate the mean number of weeks that patients exercise regularly following cardiac surgery. Assume that the standard deviation in the number of weeks cardiac patients exercise regularly following surgery is 6.3 weeks. If a sample of 40 cardiac patients is followed, and the number of weeks in which each patient exercises regularly is recorded, what is the probability that the sample mean will be no more than 1 week higher than the true mean?

Explanation / Answer

following cardiac surgery, patients are encouraged to exercise regularly (assume that regular exercise is defined as exercising on 3 or more days per week). A physician suspects that the patients exercise regularly immediately following cardiac surgery but tend to reduce, even stop exercising completely, over time. An investigation is planned to estimate the mean number of weeks that patients exercise regularly following cardiac surgery. Assume that the standard deviation in the number of weeks cardiac patients exercise regularly following surgery is 6.3 weeks. If a sample of 40 cardiac patients is followed, and the number of weeks in which each patient exercises regularly is recorded, what is the probability that the sample mean will be no more than 1 week higher than the true mean?

standard error = s.d./sqrt(n) = 6.3/sqrt(40) = 0.9961

Z = (X - true mean) / 0.99 = (true mean + 1 - true mean) / 0.99 = 1/0.9961 =1.00

P( mean x < truemean+1)

=P( z <1)

= 0.8413