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 she wishes the estimate to be within two percentage points with 90​% ​confidence, assuming that

​(a) she uses the estimates of 21.7​% male and 19.5​% female from a previous​ year?

n=__ ​(Round up to the nearest whole​ number.)

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

n=___ ​(Round up to the nearest whole​ number.)

Answer 1

Solution:

(a)

Given:

The margin of error for difference in proportion is define as,

Where,

The required sample size is,

(b)

Now, since the point estimate for the male and female proportions are not given, in this case the point estimate for each male and female will be 0.50.

Now the sample size will be

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