In a survey of 1002 people, 70 % said that they voted in a...

In a survey of 1002 people, $70 \%$ said that they voted in a recent presidential election (based on data from ICR Research Group). Voting records show that $61 \%$ of eligible voters actually did vote. a. Find a $98 \%$ confidence interval estimate of the proportion of people who say that they voted. b. Are the survey results consistent with the actual voter turnout of $61 \%$ ? Why or why not?

In a survey of 1002 people, $70 \%$ said that they voted in a recent presidential election (based on data from ICR Research Group). Voting records show that $61 \%$ of eligible voters actually did vote.
a. Find a $98 \%$ confidence interval estimate of the proportion of people who say that they voted.
b. Are the survey results consistent with the actual voter turnout of $61 \%$ ? Why or why not?

Key Concepts

Assessment of Consistency

This involves comparing the constructed confidence interval to an external or known value (such as actual voter turnout) to see if the known value falls within the interval. If it does not, it suggests that the sample result might not be consistent with the actual known proportion.

Margin of Error

The margin of error is determined by multiplying the critical value by the standard error. It reflects the maximum expected difference between the true population proportion and the sample proportion within the specified confidence level.

Standard Error of a Proportion

The standard error quantifies the variability of the sample proportion and is calculated as the square root of [p(1 - p) divided by the sample size]. It is essential for determining how much the sample estimate is likely to fluctuate from the true population proportion.

Confidence Interval for a Proportion

This concept involves estimating the range within which the true proportion of a population characteristic (such as a voting rate) lies, based on a sample. It is computed by taking the sample proportion and adding and subtracting the margin of error, which reflects the uncertainty due to sampling variability.

Critical Value

A critical value is the cutoff point on the standard normal distribution that corresponds to the desired confidence level (for example, 98%). It is used to scale the standard error to determine the margin of error for the confidence interval.

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