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 marijuana should be legal or illegal, 0.47 said "legal" (n = 100).

Confidence interval using percentages

For calculating interval using percentages, the following conditions are met:-

i. Simple random sampling method is used.

ii. For sufficiently large samples, it should includes at least 10 successes and 10 failures.

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{0.47(1-0.47)/100} {/eq}

{eq}S_{e} {/eq} = 0.0499 {eq}\approx {/eq} 0.05

Therefore, the 95% confidence interval is 0.47 - 2 (0.05) = 0.37 to 0.47 + 2 (0.05) = 0.57.


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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