Question

A researcher wishes to? estimate, with 9090?% ?confidence, the population proportion of adults who say chocolate is their favorite ice cream flavor. Her estimate must be accurate within 33?% of the population proportion.

?(a) No preliminary estimate is available. Find the minimum sample size needed.

?(b) Find the minimum sample size? needed, using a prior study that found that 4444?% of the respondents said their favorite flavor of ice cream is chocolate.

?(c) Compare the results from parts? (a) and? (b).

Answer 1

a)

here margin of error E =	0.03
for90% CI crtiical Z          =	1.6449
estimated proportion=p=	0.500
required sample size n =	p*(1-p)*(z/E)2=	752.00

( please try n=748 if above comes wrong due to rounding error)

b)

here margin of error E =	0.03
for90% CI crtiical Z          =	1.6449
estimated proportion=p=	0.440
required sample size n =	p*(1-p)*(z/E)2=	741.00

( please try n=737 if above comes wrong due to rounding error)

c) having an estimate reduces sample size requirement)