Question

A poll wants to construct a 95% confidence interval for the proportion of adults who believe that economic conditions are getting better. A poll taken in July estimates this proportion to be 0.33 using this estimate what sample sizes needed so that the confidence interval will have a margin of error of .081

Answer 1

Solution :

Given that,

= 0.33

1 - = 1 - 0.33 = 0.67

margin of error = E = 0.081

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 ( see the 0.025 value in standard normal (z) table corresponding z value is 1.96 )

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

= (1.96 / 0.081)2 * 0.33* 0.67

= 129.45

Sample size = 130 rounded