Question

A physical therapist wants to determine the difference in the proportion of men and women who participate in regular sustained physical activity. What sample size should be obtained if

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wishes the estimate to be within

twotwo

percentage points with

9090​%

​confidence, assuming that​(a)

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uses the estimates of

21.621.6​%

male and

19.719.7​%

female from a previous​ year?​(b)

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does not use any prior​ estimates?

​(a)

nequals=nothing

​(Round up to the nearest whole​ number.)

Answer 1

a) Given that, p₁ = 0.216 and p₂ = 0.197

margin of error ( E ) = 2% = 0.02

A 90% confidence level has significance level = 0.01 and critical value is,

We want to find, the sample size ( n ),

Therefore, required sample size is 2216

b) Assuming that she does not use any prior estimates.

So, p₁ = p₂ = 0.5 and sample size ( n ) is,

Therefore, required sample size is 3283