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In 2012 GSS respondents were asked if they were afraid to walk in their neighborhood at night and...

Question:

In 2012 GSS respondents were asked if they were afraid to walk in their neighborhood at night and could respond yes or no. Approximately {eq}34 \% {/eq} ({eq}445 {/eq} of {eq}1,300 {/eq}) responded they were afraid. Calculate and interpret a {eq}95 \% {/eq} confidence interval for this parameter estimate.

Confidence Interval:

The confidence interval comes under the theory of estimation. It provides an estimate of the population parameter, i.e., population proportion on the basis of the sample proportion. An excel function, NORMINV() is used for the confidence coefficient.

Answer and Explanation:

Given that,

Sample proportion, {eq}\hat{p} = 0.34 {/eq}


The 95% confidence interval for the population proportion is defined as:

{eq}\hat{p} \pm z_{0.05/2}\times \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}} {/eq}


Excel function for the confidence coefficient:

=NOMRINV(0.05/2,0,1)


{eq}0.34 \pm 1.96\times \sqrt{\dfrac{0.34(1-0.34)}{1300}}\\ (0.314, \ 0.366) {/eq}

The true proportion of the population who were afraid to walk in their neighborhood lies in the above confidence interval.


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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