Question

You are a politician and would like to know how the percentage of people that support your proposition. You go out and get a random sample of 1000 register voters that are likely to vote in the upcoming election and find out that 300 of them will vote for your proposition. Based upon your observed sample proportion, how many voters would you need to sample if you wanted your margin of error to be 7% with 99% confidence? a) 57 b) 871 c) 8068 d) 285 U O D

Answer 1

Solution :

Given that,

$\hat p$ = x/n=300/1000=0.3

1 - $\hat p$ = 1 - 0.3 = 0.7

margin of error = E = 7% = 0.07

At 99% confidence level the z is,

$\alpha$ = 1 - 99%

$\alpha$ = 1 - 0.99 = 0.01

$\alpha$/2 = 0.005

Z$\alpha$/2 = 2.58    ( Using z table )

Sample size = n = (Z$\alpha$/2 / E)2 * $\hat p$ * (1 - $\hat p$ )

= (2.58 / 0.07)2 * 0.3 * 0.7

=285

Sample size = 285

d