Question

Out of 500 people sampled, 235 preferred Candidate A. Based on this, find a 95% confidence level for the true proportion of the voting population (P) prefers Candidate A. Give your answers as decimals, to three places <pく 20 Points possible:1

Answer 1

Solution :

Given that,

n = 500

x = 235

$\hat p$ = x / n = 235 / 500 = 0.470

1 - $\hat p$ = 1 - 0.470 = 0.530

At 95% confidence level the z is ,

$\alpha$ = 1 - 95% = 1 - 0.95 = 0.05

$\alpha$ / 2 = 0.05 / 2 = 0.025

Z_$\alpha$/2 = Z_0.025 = 1.96

Margin of error = E = Z_{$\alpha$ / 2} * $\sqrt$(($\hat p$ * (1 - $\hat p$)) / n)

= 1.96 * ($\sqrt$((0.470 * 0.530) / 500)

= 0.044

A 95% confidence interval for population proportion p is ,

$\hat p$ - E < P < $\hat p$ + E

0.470 - 0.044 < p < 0.470 + 0.044

0.426 < p < 0.514