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Chapter 3: Problem 73

Give information about the proportion of a sample that agrees with a certain statement. Use StatKey or other technology to estimate the standard error from a bootstrap distribution generated from the sample. Then use the standard error to give a \(95 \%\) confidence interval for the proportion of the population to agree with the statement. StatKey tip: Use "CI for Single Proportion" and then "Edit Data" to enter the sample information. In a random sample of 400 people, 112 agree and 288 disagree.

Short Answer

Expert verified
The Bootstrap distribution can be used to estimate the 95% confidence interval, which will indicate the range where the true proportion of the population that agrees with the statement is likely to be. This will be done by calculating the sample proportion, generating a bootstrap distribution from it, estimating the standard error, and calculating the confidence interval from that error.

Step by step solution

01

Determine the Proportion

Firstly, calculate the sample proportion. This is obtained by dividing the number who agree (112) by the total sample size (400). This will give the proportion of people in the sample who agree with the statement.
02

Generate the Bootstrap Distribution

Next, use StatKey or a similar tool to generate a bootstrap distribution. Enter the sample details into the software (112 agree, 288 disagree). The software will use this sample to generate a bootstrap distribution and an estimate of the standard error. It's important to note that the standard error is a measure of the precision of the bootstrap estimate. The smaller the standard error, the more accurate the estimate.
03

Calculate the Confidence Interval

Finally, calculate the 95% confidence interval using the standard error. A 95% confidence interval can be interpreted as a range within which we are 95% confident that the true population proportion lies. In the software, select 'CI for Single Proportion', which will calculate the confidence interval based on the simulated bootstrap distribution and standard error that were previously computed.

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Give information about the proportion of a sample that agree with a certain statement. Use StatKey or other technology to find a confidence interval at the given confidence level for the proportion of the population to agree, using percentiles from a bootstrap distribution. StatKey tip: Use "CI for Single Proportion" and then "Edit Data" to enter the sample information. Find a \(99 \%\) confidence interval if, in a random sample of 1000 people, 382 agree, 578 disagree, and 40 can't decide.
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