Question

Suppose you wish to know the proportion of registered voters in CA who support a particular ballot measure. Further suppose that some initial estimates indicate that the proportion of registered voters who support the measure is approximately 0.58. Determine the sample size required to estimate the true proportion if you want to be 98% confident that your estimate of the proportion is within 0.02 (two percentage points).

You need to sample _____ registered voters in order to be 98% confident that your estimate is not off my more than 2%.

Answer 1

Answer: 3295

Explanation:

We know that the formula we use to find the sample size , if prior proportion is available :-

`n=p(1-p)((z_(\alpha/2))/(E))^2`

Given : The approx proportion of registered voters who support the measure is : p= 0.58

Margin of error : E=0.02

Critical value for 98 percent confidence :
`z_(\alpha/2)=2.326`

Required sample will be :

`n=(0.58)(1-0.58)((2.326)/(0.02))^2=3294.858084\approx3295`

Hence, You need to sample 3295 registered voters in order to be 98% confident that your estimate is not off my more than 2%.