Question

750 out of 2586 people surveyed are not saving for retirement. Use these data to construct a 90% confidence interval for the percentage of people who are not saving for retirement. Also, find the margin of error. Round your answers to 3 decimal places.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 750 / 2586 = 0.29

Z_/2 = 1.645

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

= 1.645 * (((0.29 * 0.71) / 2586)

= 0.015

Margin of error = 0.015

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.29 - 0.015 < p < 0.29 + 0.015

0.275 < p < 0.305

(0.275 , 0.305)