Question

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

Answer 1

Answer:

467 voters

Step-by-step 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 $\frac{\alpha}{2}$

$z^* = 1.96$ --- the critical level

So, we have:

$n = p * (1 - p) * (\frac{z^*}{E})^2$

$n = 0.65 * (1 - 0.65) * (\frac{1.96}{0.0433})^2$

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

$n = 0.65 * 0.35 * 2052.1$

$n = 466.9$

$n = 467$ --- approximated