Question

A polling agency is deciding how many voters to poll.

1. The agency wants to estimate the percentage of voters in favour of extending tax cuts, and it wants to provide a margin of error of no more than 1.8 percentage points. Using 95% confidence, how many respondents must the agency poll?

2. If the margin of error is to be no more than 1.7%, with 95% confidence, should the sample be larger or smaller than that determined in part a? Explain your reasoning.

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c. If the degree of confidence were lowered to 90%, with the margin of error no more than 1.8%, would that require a larger or a smaller sample size than the result for part a?

Answer 1

1)for 1.8% margin of error

here margin of error E =	0.018
for95% CI crtiical Z          =	1.960
estimated proportion=p=	0.500
required sample size n =	p*(1-p)*(z/E)2=	2965.00

if margin of error is reduced from 1.8% to 1.7% ; sample size requirement will increase to increase the precision ;also from formula ; sample size required is inversely proportional to margin of error square root

c)

here margin of error E =	0.018
for90% CI crtiical Z          =	1.645
estimated proportion=p=	0.500
required sample size n =	p*(1-p)*(z/E)2=	2088.00