Question

A construction engineer wanted to conduct research study and wishes to estimate, with 90% confidence, the proportion of people living in metro manila who own a home built by a constructor. A previous study showed that 35% of those interviewed had their houses built by a construction firm. The engineer wishes to be accurate within 2.5% of the true proportion. Find the minimum sample size necessary.

Answer 1

Solution :

Given that,

$\hat p$ = 35% = 0.35

1 - $\hat p$ = 1 - 0.35 = 0.65

margin of error = E = 2.5% = 0.025

At 90% confidence level the z is ,

$\alpha$ = 1 - 90% = 1 - 0.90 = 0.10

$\alpha$ / 2 = 0.10 / 2 = 0.05

Z_$\alpha$/2 = Z_0.05 = 1.645

sample size = n = (Z_{$\alpha$ / 2} / E )² * $\hat p$ * (1 - $\hat p$ )

= (1.645 / 0.025)² * 0.35 * 0.65

= 985

sample size = 985