Answer to Question #182603 in Statistics and Probability for Tanya

Question #182603

A pollster wishes to estimate the true proportion of U.S. voters who oppose capital punishment. How many voters should be surveyed in order to be 95% confident that the true proportion is estimated to be within 5%?

1
Expert's answer
2021-05-02T09:47:58-0400

To obtain the sample size,

n=(z)2p^q^M.E2n=\frac{(z^*) ^2\hat p\hat q} {M.E^2}

Where z* is the corresponding z score

P is the proportion of voters

q is the proportion of non-voters

M. E is the margin of error.

For 95%confidence interval, the z score is 1.96.

n=(1.96)2p^q^0.052n=\frac{(1.96)^2\hat p\hat q} {0.05^2}

n=1536.64pq

Assuming that the proportion of voters is 0.5 then non-voters are 0.5.

n=1536.64pq

≈385 voters


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