Question

A CBS News poll conduced in the United States November 16-19, 2012 asked, “Do you think the use of marijuana should be legal or not?” In the nationwise poll of n = 1100 adults, 47% said they favored legalization. (SHOW YOUR WORK)

(a) Calculate a 99% con?dence interval that estimates the proportion of all voters who favor legalizing marijuana. Give your ?nal answer as percents rounded to two decimal places.

(b) On the basis of this con?dence interval, is it reasonable to infer that in 2012 more than half of all Americans favored legalization of marijuana? Why or why not? Explain.

Answer 1

a) From the standard normal tables, we have:

P( -2.576 < Z < 2.576 ) = 0.99

Now the standard error here first computed as:

The confidence interval here is computed as:

This is the required 99% confidence interval for the proportion of all voters who favor legalizing marijuana

b) We cannot infer from the given confidence interval that in 2010 more than half of all Americans favored legalization of marijuana, because the whole confidence interval is not above the 0.5 value but 0.5 lies in the given confidence interval.