Question

the figure to the right shows the results of a survey in which 3000 college graduates from the year 2016 were asked questions about employment. construct 99% confidence intervals for the population proportion of college students who gave each response. employment college students responses to questions about employment expect to stay at first employer for 3 or more years 70% completed an apprenticeship or internship 68% employed in field of study 63% feel underemployed 48% prefer to work for a large company 14% (round to three decimal places as needed) the 99% confidence interval for the proportion of college students that have completed an apprenticeship or internship is (0.658, 0.702) (round to three decimal places as needed) the 99% confidence interval for the proportion of college students that are employed in their field of study is (0.607, 0.653) (round to three decimal places as needed) the 99% confidence interval for the proportion of college students that feel underemployed is (□,□)

Explanation:

Step1: Determine the formula for confidence interval

The formula for a confidence interval for a population proportion \(p\) is \(\hat{p}\pm z_{\alpha/2}\sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}\), where \(\hat{p}\) is the sample proportion, \(n\) is the sample size, and \(z_{\alpha/2}\) is the z - score. For a \(99\%\) confidence interval, \(\alpha=1 - 0.99 = 0.01\), and \(\alpha/2=0.005\). From the standard normal table, \(z_{\alpha/2}=z_{0.005} = 2.576\). Here \(n = 3000\).

Step2: Calculate for the "feel underemployed" response

Given \(\hat{p}=0.48\) (since \(48\%=0.48\)). First, calculate the margin of error \(E\):

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Step3: Calculate the confidence interval

The confidence interval is \(\hat{p}-E

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Answer:

\((0.457,0.504)\) (rounded to three decimal places)