Question

In a poll to estimate presidential popularity, each person in a random sample of 1,230 voters was asked to agree with one of the following statements:

The president is doing a good job.

The president is doing a poor job.

I have no opinion.

A total of 675 respondents selected the first statement, indicating they thought the president was doing a good job.

Construct a 99% confidence interval for the proportion of respondents who feel the president is doing a good job. (Round your answers to 3 decimal places.)

Based on your interval in part (a), is it reasonable to conclude that a majority of the population believes the president is doing a good job?

Yes

No

Answer 1

a)

Sample proportion = 675 / 1230 = 0.549

99% confidence interval for p is

- Z * sqrt( ( 1 - ) / n) < p < + Z * sqrt( ( 1 - ) / n)

0.549 - 2.5758 * sqrt( 0.549 * 0.451 / 1230) < p < 0.549 + 2.5758 * sqrt( 0.549 * 0.451 / 1230)

0.512 < p < 0.586

99% CI is (0.512 , 0.586)

Since 0.50 does not contain in confidence interval ( and all values of the confidence interval are

greater than 0.50) , we have sufficient evidence to support the claim.

Yes