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A physical therapist wants to determine the difference in the proportion of men and women who...

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Statistics

A physical therapist wants to determine the difference in theproportion of men and women who participate in regular sustainedphysical activity. What sample size should be obtained if he wishesthe estimate to be within two percentage points with 99​%​confidence, assuming that

​(a) he uses the estimates of 22.6​% male and 18.9​% female froma previous​ year?

n=____

​(b) he does not use any prior​ estimates?

n=____

Answer & Explanation Solved by verified expert
4.3 Ratings (572 Votes)

a)

p1          = 0.226
q1=1-p1= 0.774
p2          = 0.189
q2=1-p2= 0.811
here margin of error E = 0.02
for99% CI crtiical Z          = 2.576
required sample size n =         (p1q1+p2q2)*(Z/E)2= 5445.00

( please try 5444 if this comes wrong)

b)

p1          = 0.5
q1=1-p1= 0.5
p2          = 0.5
q2=1-p2= 0.5
here margin of error E = 0.02
for99% CI crtiical Z          = 2.576
required sample size n =         (p1q1+p2q2)*(Z/E)2= 8295.00

( please try 8294 if this comes wrong)
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