A researcher would like to estimate p the proportion of US a

A researcher would like to estimate p, the proportion of U.S. adults who support recognizing civil unions between gay or lesbian couples. Due to a limited budget, the researcher obtained opinions from a random sample of only 1,000 U.S. adults.With this sample size, the researcher can be 95% confident that the obtained sample proportion will differ from the true proportion (p) by no more than which of the following percentages (answers are rounded)?

Solution

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.5          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.015811388          
              
Now, for the critical z,              
alpha/2 =   0.025          
Thus, z(alpha/2) =    1.959963985          
Thus,              

Margin of error = z(alpha/2)*sp =    0.030989752   

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Thus, your answer, must be GREATER THAN 0.03099 or 3.099% [ANSWER]          

Please choose the option that satisfies the condition above.