Question

A sociologist wants to construct a 95% confidence interval for the proportion of children aged 8–12 living in New York who own a cell phone. A survey estimated the nationwide proportion to be 0.56. What sample size is needed so that the confidence interval will have a margin of error of 0.02? (Provide your answer as a whole number).

Answer #1

Solution :

Given that,

= 0.56

1 - = 1 - 0.56= 0.44

margin of error = E = 0.02

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 / 0.02)2 * 0.56 * 0.44

= 2366.42

Sample size =2366 rounded

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