Question

In the nationwide poll of n = 1,100 adults, 38% said that they favored legalization. The margin of error for the 95% confidence level was given as 3%. (a) Find a 95% confidence interval estimate of the percentage of American adults who favored the legalization of marijuana at the time of the poll.

Answer 1

Answer: (35% , 41%)

Explanation:

The confidence interval for population proportion is given by :-

`(\overline{p}- E,\ \overline{p}+ E)` , where
`\overline{p}` = sample proportion.

and E = margin of error.

Given : The percentage of adults favored legalization :
`\overline{p}=38\%`

Margin of error for the 95% confidence level : E= 3%

Then, the 95% confidence interval estimate of the percentage of American adults who favored the legalization of marijuana at the time of the poll. will be :

(38%-3% , 38%+3%)= (35% , 41%)

Hence, the 95% confidence interval estimate of the percentage of American adults who favored the legalization of marijuana at the time of the poll = (35% , 41%)