Question

Solution :

Given that,

Point estimate = sample proportion = $\hat p$ = x / n = 106 / 160 = 0.663

1 - $\hat p$ = 1 - 0.663 = 0.337

Z$\alpha$/2 = Z0.05 = 1.645

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

= 1.645 ($\sqrt$((0.663 * 0.337) / 160)

= 0.061

A 90% confidence interval for population proportion p is ,

$\hat p$ ± E

= 0.663 ± 0.061

= ( 0.602, 0.724 )

lower limit = 0.602

upper limit = 0.724

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