How many voters should be sampled for a 95% confidence interval? Round up to the nearest whole number.

Question

asked Oct 26, 2022 78.1k views

1 Answer

Sam Jarman · Answer 1 · 2022-11-01T02:52:00+0000

Answer:

467 voters

Explanation:

Given

See attachment for complete question

Required

Sample size at 95% confidence interval

From the attachment, we have:

$p = 65\% = 0.65$

$E = 4.33\% = 0.0433$

CL = 0.95

$\alpha = 0.05$ i.e. 1 - CL

First, we calculate the critical level

At
CL = 0.95 and
$(\alpha)/(2)$

z^* = 1.96 --- the critical level

So, we have:

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

n = 0.65 * (1 - 0.65) * ((1.96)/(0.0433))^2

n = 0.65 * (1 - 0.65) * (45.3)^2

n = 0.65 * 0.35 * 2052.1

n = 466.9

n = 467 --- approximated