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In a survey of 314 job recruiters, 46% said that they had reassessed a job candidate after viewing his/her social media profile and content. (This includes both positive and negative reassessments of the job candidate.) Construct a 90% confidence interval for the proportion of job recruiters who reassessed a job candidate after viewing his/her social media content.

User Eric Urban
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Answer:

The 90% confidence interval for the proportion of job recruiters who reassessed a job candidate after viewing his/her social media content is (0.4137, 0.5063).

Explanation:

In a sample with a number n of people surveyed with a probability of a success of
\pi, and a confidence level of
1-\alpha, we have the following confidence interval of proportions.


\pi \pm z\sqrt{(\pi(1-\pi))/(n)}

In which

z is the zscore that has a pvalue of
1 - (\alpha)/(2).

In a survey of 314 job recruiters, 46% said that they had reassessed a job candidate after viewing his/her social media profile and content. (This includes both positive and negative reassessments of the job candidate.)

This means that
n = 314, \pi = 0.46

90% confidence level

So
\alpha = 0.1, z is the value of Z that has a pvalue of
1 - (0.1)/(2) = 0.95, so
Z = 1.645.

The lower limit of this interval is:


\pi - z\sqrt{(\pi(1-\pi))/(n)} = 0.46 - 1.645\sqrt{(0.46*0.54)/(314)} = 0.4137

The upper limit of this interval is:


\pi + z\sqrt{(\pi(1-\pi))/(n)} = 0.46 - 1.645\sqrt{(0.46*0.54)/(314)} = 0.5063

The 90% confidence interval for the proportion of job recruiters who reassessed a job candidate after viewing his/her social media content is (0.4137, 0.5063).

User Gayan Kalhara
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