Question

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.

Answer 1

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).