Question

A pollster wishes to estimate, with 95% confidence, the proportion of people who approve of how President Trump is performing his job.

Find the minimum sample size necessary to achieve a margin of error of less than 3%.

1. Assuming no previous estimates are available. Round your answer up to the next integer.
2. Assuming a previous estimate of 0.90. Round your answer up to the next integer

Answer 1

a)
The following information is provided,
Significance Level, α = 0.05, Margin of Error, E = 0.03

The provided estimate of proportion p is, p = 0.5
The critical value for significance level, α = 0.05 is 1.96.

The following formula is used to compute the minimum sample size required to estimate the population proportion p within the required margin of error:
n >= p*(1-p)*(zc/E)^2
n = 0.5*(1 - 0.5)*(1.96/0.03)^2
n = 1067.11

n = 1068

b)
The provided estimate of proportion p is, p = 0.9
The critical value for significance level, α = 0.05 is 1.96.

n >= p*(1-p)*(zc/E)^2
n = 0.9*(1 - 0.9)*(1.96/0.03)^2
n = 384.16

n = 385