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# Estimation: Confidence Intervals and Sample Size

1) In a poll to estimate presidential popularity, each person in a random sample of 1,000 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 560 respondents selected the first statement, indicating they thought the President was doing a good job.

A. Construct a 95 percent confidence interval for the proportion of respondents who feel the President is doing a good job.

B. Based on your interval in part (a), is it reasonable to conclude that a majority (more than half) of the population believes the President is doing a good job?

2) The Tennessee Tourism Institute (TTI) plans to sample information center visitors entering the state to learn the fraction of visitors who plan to camp in the state. Current estimates are that 35 percent of visitors are campers. How large a sample would you take to estimate.

#### Solution Preview

1.) In a poll to estimate presidential popularity, each person in a random sample of 1,000 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 560 respondents selected the first statement, indicating they thought the President was doing a good job.

A. Construct a 95 percent confidence interval for the proportion of respondents who feel the President is doing a good job.

95% Confidence limits for proportions=
p= 56.00% = 56/1000
q=1-p= 44.00%
n=sample size= 1000
s p=standard error of proportion= square root of (pq/n)= 1.57% = square root of ( 56.% * 44.% / 1000)
Confidence level= 95%
Significance level= a (alpha) = 5% =100% -95%
No of tails= 2 ...

#### Solution Summary

The confidence interval and sample size required are calculated for 2 estimation problems. Calculations are provided in plain text and formatted with formula in the attached Excel file.

\$2.19