What is the relevant statistic?

Question

In an August 2012 Gallup survey of 1,012 randomly selected U.S. adults (age 18 and over), 53% said that they were dissatisfied with the quality of education students receive in kindergarten through grade 12. They also report that the "margin of sampling error is plus or minus 4%."

Answer 1

Hi Madeline,
 
         This poll is interested in the PROPORTION of U.S. adults, as represented in this random sample of 1012, that are dissatisfied with the quality of education students receive in K-12.  So the population parameter of interest is the proportion, denoted by the single letter "p"...in this particular case, we can estimate this population parameter with the relevant sample statistic for the proportion, denoted "p-hat," a "p" with a caret over it.  Here,
 
                               p-hat =  0.53  +/- 0.04
 
Hope that helps!
 
David F. from Modesto, CA

Answer 2

We use the z statistic to calculate the margin of error. the error E = z(alpha/2)/(2 x sqrt(n)), where n equals the number in the survey.

 

We can back calculate to z from the data. 04 = z/(2 x sqrt 1012)  so z = 2.54, the z score for 99% confidence. The total margin of error is 8%, 4 up and 4 down, and alpha = 0.01

 

Dorene O