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

Answer:

the margin of error is 0.029

Step-by-step 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

$= Z\alpha / 2 \times \frac{((\hat p \times (1 - \hat p ))}{(\sqrt / n)} \\\\= 1.96 (\sqrt \frac{ (0.659 \times 0.341)}{(1019)} \\\\= 0.029$

Hence, the margin of error is 0.029