Question

 A polling firm called 1,000 likely voters to ask about their political preferences. Of those polled, 520 indicated that they would vote for the incumbent candidate.

 

1. Determine the point estimate for the proportion of voters in the election district who will vote for the incumbent.

2. What is the sampling distribution for p in this example?

3. Approximately how many voters must be polled for a margin of error equal to .01, assuming a confidence level of 95%? Show your work.

Answer 1

n = 1000

x = 520

a)

p̂ = x/n = 0.52

Point estimate, p̂ = x/n = 0.52

b)

Sampling distribution of p̄ = 0.52

c)

Proportion, p = 0.52

Margin of error, E = 0.01

Confidence Level, CL = 0.95

Significance level, α = 1 - CL = 0.05

Critical value, z = NORM.S.INV(0.05/2) = 1.9600

Sample size, n = (z² * p * (1-p)) / E² = (1.96² * 0.52 * 0.48)/ 0.01²

= 9588.2812

= 9589