Question

Find the sample size needed to estimate the percentage of Democrats among registered voters in Texas. Use a 0.01 margin of error, and use a confidence level of 96% and assume LaTeX: \hat{p}

p
^
=0.28.

Answer 1

Explanation:

Hello!

You have to determine the sample size to take to estimate the population proportion of Democrats among registered voters in Texas for a 96% interval with a margin of error of 0.01 and sample proportion p'= 0.28

The interval for the population proportion is

p' ±
`Z_(1-\alpha /2)`*
`\sqrt{(p'(1-p'))/(n) }`

The margin of error of the interval is:

d=
`Z_(1-\alpha /2)`*
`\sqrt{(p'(1-p'))/(n) }`

`(d)/(Z_(1-\alpha /2))= \sqrt{(p'(1-p'))/(n) }\\((d)/(Z_(1-\alpha /2)) )^2= (p'(1-p))/(n) \\n*((d)/(Z_(1-\alpha /2)) )^2= p'(1-p)\\n= p'(1-p)*((Z_(1-\alpha /2))/(d) )^2\\`

`Z_(1-\alpha /2)= Z_(0.98)= 2.054`

`n= 0.28*(1-0.28)*((2.054)/(0.01) )^2= 8505.33`

n= 8506 voters

I hope this helps!