Question

In a recent poll of 1018 adults aged 18 and over in a​ country, 4​% of respondents said they were very uncomfortable with their ability to make their monthly payments on their current debt during the next three months. Find a 95​% confidence interval for the proportion of the adult population that feels this way.

Answer 1

Solution :

Given that,

n = 1018

Point estimate = sample proportion = =0.04

1 - = 1-0.04=0.96

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table )   

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.96 (((0.04*0.96) /1018 )

E = 0.0120

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.04-0.0120< p <0.04+ 0.0120

0.0280< p < 0.0520

The 95% confidence interval for the population proportion p is : 0.0280,0.0520