Question

You survey 1012 Americans and find that 587 support legalizing marijuana. What is your estimate of the percent of Americans who support legalizing marijuana? What is a 95% confidence interval on your estimate?

Answer 1

Solution :

Given that,

n = 1012

x = 587

Point estimate = sample proportion = = x / n = 587 / 1012 = 0.580

1 - = 1 - 0.580 = 0.420

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.96 * (((0.580 * 0.420) / 1012)

= 0.030

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.580 - 0.030 < p < 0.580 + 0.030

0.550 < p < 0.610

The 95% confidence interval for the population proportion p is : (0.550 , 0.610)