Question

The 2004 presidential election exit polls from the critical state of Ohio provided the following results. There were 2020 respondents in the exit polls and 768 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 that voted for George Bush. Round the answers to 3 decimal places.

Answer 1

Answer:

0.1864 < p < 0.2215

Explanation:

To calculate and construct the 95% confidence interval for the population proportion, it's necessary to use the normal distribution of one sample proportion.

Excel function of normal distribution NORMINV() ---> value of confidence coefficient.

$\\ p = \frac{x}{n}p = \frac{412}{2020\\}\\ \\p = 0.204\\\\\\p +/- z_{0.05/2} X \sqrt{\frac{p (1-p)}{n} }  

Excel function:

NORMINV (0.05/2,0,1)

\\\\z_{0.05} = 1.96\\ \\0.204 +/- 1.96 X \sqrt{\frac{0.204 (1-0,204}{2020} }\\ \\0.1864 < p < 0.2215$