Expert: Jenny - 10/14/2004

Question
I am having trouble with the entire problem..my teacher is not the greatest in the world and i've done everything i can to try and figure it out...i just dont get it...

If you can't help me its ok i have a test on monday and this is my last hope at trying to understand...

Here's the problem:

When we hear results of polls and surveys we often get results like, 57% approve of the presidents performance plus or nimue 3 percentage points. the 3% is the possible error of the estimate. It comes from the statistics formula
      E=1.96(.25/N)raised to the (1/2)power

E=the error in the estimate
N= the sample size

A) solve this equation.  Get N by itself on one side of the equation, you will still have an E in the result
B) how large my N be if we want E to be AT MOST 3% or .03? (Hint: the larger N is the lower E will be.

the only thing i even believe i know how to do it
     E=1.96(.25/N)raised to the (1/2)power
     E=1.96(.5/N to the (1/2power))
   I just distributed the (1/2)...honestly that is all i know how to do..and i don't even know if it is right! PLEASE HELP!

Answer
Hi Lisa,

Let's solve for N:

E=1.96(.25/N)^(1/2)

The first thing we can do is divide both sides by 1.96.  This will give us:

(E/1.96)=(.25/N)^(1/2)

Now, raising something to the 1/2 power is the same thing as taking the square root.  So what you really have is:

(E/1.96)=sqrt(25/N)

If we square both sides, we can get rid of the square root:

(E/1.96)^2=25/N

Multiply both sides by N to get rid of the fraction:

N(E/1.96)^2=25

And finally, divide both sides by (E/1.96)^2:

N=25/(E/1.96)^2

So, that's part (A). For part (B): how large will N be if we want E to be AT MOST 3% or .03? (Hint: the larger N is the lower E will be.)

We can put in .03 for E and see what we get for N, for starters:

N=25/(.03/1.96)^2
N=25/(.015)^2
N=25/(.0002343)
N=106700.8

So, if E gets smaller as N gets bigger, then N has to be at least 106700.8

Good luck with this problem and on your test!