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:

1.	The president is doing a good job.
2.	The president is doing a poor job.
3.	I have no opinion.

A total of 525 respondents selected the first statement, indicating they thought the president was doing a good job.

a.	Construct a 98% confidence interval for the proportion of respondents who feel the president is doing a good job. (Use Student's t Distribution Table.) (Round your answers to 3 decimal places.)

Confidence interval for the proportion is  up to  .

b.	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?
	No Yes

Answer 1

P = 525/1230 = x/n = 0.43 Q = 1 - P = 1 - 0.43 = 0.57 a) 98% confidence interval: - Standard error (SE) = squareroot PQ/n = squareroot (0.43) (0.57)/1230 = 0.014 P plusminus Z_alpha squareroot PQ/n 0.43 plusminus 2.33 times 0.014 0.43 plusminus 0.03 (0.39, 0.46)