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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.

Of the individuals in a survey, 0.40 still live in the same city they lived in when they were 16 years of age (n = 225).

Estimating Proportions with confidence

Estimating Proportions with confidence is calculated by multiplying the multiplier with the standard error and adding or subtracting with sample estimate. The proportion estimated using confidence interval lies within 0 and 1.

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{0.40(1-0.40)/225} {/eq}

{eq}S_{e} {/eq} = 0.033 {eq}\approx {/eq} 0.03

Therefore, the 95% confidence interval is 0.40 - 2 (0.03) = 0.34 to 0.40 + 2 (0.03) = 0.46.


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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