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The following proportion is based on a survey response. For the following proportion, use the +/-...

Question:

The following proportion is based on a survey response.

For the following proportion, use the {eq}\pm {/eq} 2 shortcut to determine the 95% confidence interval.

When asked if they are a government employee, 0.20 said "yes" (n = 121).

Confidence interval using proportions

The process for finding the confidence interval using proportions is similar to the process for finding the confidence interval using the mean, but the formulas are a little different. The different formulas are based on the central limit theorem.

Answer and Explanation:

First, we calculate the standard error of proportion, {eq}S_{e} {/eq}

{eq}S_{e} = \sqrt{p(1-p)/n} {/eq}

{eq}S_{e} = \sqrt{0.20(1-0.20)/121} {/eq}

{eq}S_{e} {/eq} = 0.036 {eq}\approx {/eq} 0.04

Therefore, the 95% confidence interval is 0.20 - 2 (0.04) = 0.12 to 0.20 + 2 (0.04) = 0.28. (0.12 to 0.28)


Learn more about this topic:

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Finding Confidence Intervals for Proportions: Formula & Example

from Statistics 101: Principles of Statistics

Chapter 9 / Lesson 8
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