A recent study indicated that 22% of the 161 women over age 55 in the study...

A recent study indicated that 22% of the 161 women over age 55 in the study were widows. Round up your answers to the next whole number for the following questions.

How large a sample must you take to be 95% confident that the estimate is within 0.04 of the true proportion of women over age 55 who are widows?

Solutions

Expert Solution

Solution :

Given that,

= 0.22

1 - = 1 - 0.22 = 0.78

margin of error = E = 4% = 0.04

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

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

Sample size = n = (Z/2 / E)2 * * (1 - )

= (1.96 / 0.04)2 * 0.22 * 0.78

= 412.0116

Sample size =412

orchestra answered 1 year ago

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