A college believes that 22% of aoolication to that school have parents who have remarried. How...

A college believes that 22% of aoolication to that school have parents who have remarried. How large a sample is needed to estimate the true poroportion of students who have parents who have remarried to within 3% with 95% confidence.

Expert Solution

Solution :

Given that,

= 22% = 0.22

1 - = 1 - 0.22 = 0.78

Margin of error = E = 3% = 0.03

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Sample size = ( Z_/2 / E)² * * (1 - )

= (1.96 / 0.03)² * 0.22 * 0.78

= 732.46 = 733

Sample size = n = 733

orchestra answered 2 years ago

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