Question

A U.S. census bureau pollster noted that in 358 random households surveyed, 233 occupants owned their own home. For a 95% confidence interval for the proportion of home owners, what is the margin of error?

Question 4 options:

	1) 0.0413
	2) 0.0494
	3) 0.0012
	4) 0.0026
	5) 0.0252

Answer 1

Solution :

Given that,

n = 358

x =233

Point estimate = sample proportion = $\hat p$ = x / n = 233/358=0.651

1 - $\hat p$ = 1 - 0.651=0.349

At 95% confidence level

$\alpha$ = 1 - 95%  

$\alpha$ = 1 - 0.95 =0.05

$\alpha$/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 ($\sqrt$((0.651*0.349) / 358)

E = 0.0494

correct option is

2)

0.0494