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?
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.
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