Question

A controversial bill is being debated in the state legislature. Representative Williams wants to estimate within 5 percentage points and with 95% confidence the difference in the proportion of her male and female constituents who favor the bill. What sample size should she obtain?

PLEASE SHOW YOUR WORK!

Answer 1

768

Explanation:

Given that:

Error margin (E) = 5% = 0.05

Confidence level = 95%

Proportion p = 0.5 (since no prior value is given) ; also n1 = n2 = sample size

n = (Z / E)^2 * (1 - p)

1 - p = 1 - 0.5 = 0.5

Zscore at 95% confidence = 1.96

n = (1.96 / 0.05)^2 * 0.5

n = 39.2^2 * 0.5

n = 1536.64 * 0.5

n = 768.32

Hence, sample size = 768 SAMPLES