Question

The 2004 presidential election exit polls from the critical state of Ohio provided the following results. The exit polls had 2020 respondents, 768 of whom were college graduates. Of the college graduates, 412 voted for George Bush.

a. Calculate a 95% confidence interval for the proportion of college graduates in Ohio who voted for George Bush.
b. Calculate a 95% lower confidence bound for the proportion of college graduates in Ohio who voted for George Bush.

Answer 1

Explanation:

The 2004 presidential election polls from critical state of Ohio reveals that out of 768 college graduates, 412 voted for Geoge Bush.

p = proportion of college graduates who voted for George Bush =
`(412)/(768) \\=0.5365`

q =
`1-p = 0.4635`

Margin of error = 95% z value * std error

=
`1.96 \sqrt{(pq)/(n) } \\=1.96*\sqrt{(0.5365*0.4635)/(768) } \\=0.0353`

Confidence interval =
`0.5435+/-0.0353\\=(0.5082, 0.5788)`

b) Lower confidence bound = 0.5082