Question

A survey of 355 working parents found 200 who said they spend too little time with their children because of work commitments.

(a)

What is the point estimate of the proportion of the population of working parents who feel they spend too little time with their children because of work commitments?

(b)

At 95% confidence, what is the margin of error?

(c)

What is the 95% confidence interval estimate of the population proportion of working parents who feel they spend too little time with their children because of work commitments?

Answer 1

Solution :

Given that,

n = 355

x = 200

a) Point estimate = sample proportion = $\hat p$ = x / n = 200 / 355 = 0.563

1 - $\hat p$ = 1 - 0.563 = 0.437

b) At 95% confidence level

$\alpha$ = 1 - 95%

$\alpha$ =1 - 0.95 =0.05

$\alpha$/2 = 0.025

Z$\alpha$/2 = Z_{0.025 = 1.960}

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

= 1.96 ($\sqrt$((0.563 * 0.437) / 355)

= 0.052

c) A 95% confidence interval for population proportion p is ,

$\hat p$ ± E  

= 0.563  ± 0.052

= ( 0.511, 0.615 )