help with math hw

Question

A television sports commentator wants to estimate the proportion of citizens who​ "follow professional​ football." Complete parts​ (a) through​ (c)

​(a) What sample size should be obtained if he wants to be within

4 percentage points with 94​%

confidence if he uses an estimate of 52​%

obtained from a​ poll?

The sample size is ___

​(Round up to the nearest​ integer.)

part a

Answer 1

margin of error is 4% or 0.04

margin of error = z critical (alpha/2) * standard error, where standard error = SQRT(phat*(1-phat)/n)), where phat is estimated proportion and n is sample size.

we want margin of error to be <= 0.04, so

z critical (alpha/2) * SQRT(phat*(1-phat)/n)) <= 0.04

alpha for 94% confidence is 0.06, so alpha/2 = 0.03, so need to look up z value for 0.03 tail, which is the z value for 0.97 probability = 1.88.

phat = 0.52, so the equation becomes:

1.88 * SQRT(0.52 * 0.48/n) <= 0.04

square both sides and solve for n, then round up to next integer value.

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