Question

A recent Gallop poll showed that 672 of 1019 adults nationwide think that marijuana should be legalized. a) Find the margin of error that corresponds to a 95% confidence interval.

Answer 1

the margin of error is 0.029

Explanation:

The computation of the margin of error is as follows;

Point estimate = sample proportion

`= \hat p` = x ÷ n = 672 ÷ 1019 = 0.659

Now

= 1 -
`\hat p`

= 1 - 0.659

= 0.341

`Z\alpha/2` = Z_0.025 = 1.96

Now

a) Margin of error = E is

`= Z\alpha / 2 * (((\hat p * (1 - \hat p )))/((\sqrt / n)) \\\\= 1.96 (\sqrt ( (0.659 * 0.341))/((1019)) \\\\= 0.029`

Hence, the margin of error is 0.029