In a poll to estimate presidential popularity, each person in a random sample of

Question

In a poll to estimate presidential popularity, each person in a random sample of 1,390 voters was asked to agree with one of the following statements:

A total of 650 respondents selected the first statement, indicating they thought the president was doing a good job.

Construct a 95% 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.)

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?

In a poll to estimate presidential popularity, each person in a random sample of 1,390 voters was asked to agree with one of the following statements:

Explanation / Answer

a) Confidence interval for population proportion is
Sample proportion +/- Confidence coefficient*Standard error of p
Sample proportion = p^ = x/n = 650/1390 = 0.47
Confidence coefficient is the critical value of z for 95% confidence level = 1.96
Standard error of p = sqrt [p*(1-p)/n]
= sqrt [0.47*0.53/1000]
Therefore, the required CI is
0.47 +/- 1.96 * sqrt [0.47*0.53/1000]
0.47 +/- 0.03
lower boundary is 0.47 - 0.03 = 0.44
upper boundary is 0.47 + 0.03 = 0.50
The CI is (0.44, 0.50)

b)  

based on this confidence interval we do not conlcude that majority of the population believes that the president is good . Because for it to be majority the proportion 0.5000 must lie in this confidence interval

Since 0.5 does not belong to this interval we conclude that no the majority of population doesnot believe that the president is good.

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