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).
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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