Question

A survey designed to obtain information on the proportion of all registered voters who are in favor of constitutional amendment requiring a balanced budget results in a sample size of n=500. Of the 500 voters sampled, 310 are in favor of such a constitutional amendment.

A.What is the point estimate of the proportion of all registered voters who are in favor of a constitutional amendment requiring a balanced budget?

B. Calculate and interpret the 99% confidence interval for p.

Answer 1

Solution :

Given that,

Point estimate = $\hat p$ = x / n = 310/ 500 = 0.62

1 - $\hat p$ = 0.38

Z$\alpha$/2 = 2.576

Margin of error = E = Z$\alpha$ / 2 * $\sqrt$ (($\hat p$ * (1 - $\hat p$ )) / n)

= 2.576 * $\sqrt$ ((0.62 * 0.38) / 500)

= 0.056

A 99% confidence interval for population proportion p is ,

$\hat p$ - E < p < $\hat p$ + E

0.620 - 0.056 < p < 0.620 + 0.056

0.564 < p < 0.676

There is 99% confidence for the population proportion of all registered voters who are in favor of a constitutional amendment requiring a balanced budge is from 0.564 to 0.676