Question

in a gallup poll of 1005 individuals, 452 thought they were worse off financially than a year ago. find and interpret the 98% confidence interval for the true proportion of individuals who feel they are worse off financially than a year ago

Answer 1

Solution :

Given that,

n = 1005

x = 452

Point estimate = sample proportion = = x / n =452 / 1005 = 0.450

1 - = 0.550

At 95% confidence level the z is ,

Z_/2 = Z _0.025 = 1.96

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

= 1.96 * (((0.450* 0.550) / 1005)

= 0.031

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.450 - 0.031 < p < 0.450 + 0.031

0.419 < p < 0.481

The 95% confidence interval for the population proportion p is : ( 0.419 , 0.481)