Question

A retirement Confidence survery of 1,141 workers and retirees in the UK 25 years of age and older conducted by employee research in January 2010 found that 495 has less than $10k in savings. Round to 4 decimals

A. Obtain a point estimate for the population proportion of workers and retirees in the UK 25 years of age and older who have less 10k saving

B Construct a 95% confidence interval for the proportion of workers and retirees in the UK 25 years of age and older who have less than 10k

Answer 1

Solution :

Given that,

Point estimate ($\hat p$) = x / n = 495 / 1141 = 0.4338

1 - $\hat p$ = 0.5662

Z$\alpha$/2 = 1.96

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

= 1.96 * $\sqrt$ ((0.4338 * 0.5662) / 1141)

= 0.0288

A 95% confidence interval for population proportion p is ,

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

0.4338 - 0.0288 < p < 0.4338 + 0.0288

0.4050 < p < 0.4626