Life after college. We are interested in estimating the proportion of graduates at a mid-sized university who found a job within one year of completing their undergraduate degree. Suppose we conduct a survey and find out that 348 of the 400 randomly sampled graduates found jobs. The graduating class under consideration included over 4500 students.
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Describe the population parameter of interest. What is the value of the point estimate of this parameter?
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Check if the conditions for constructing a confidence interval based on these data are met.
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Calculate a 95% confidence interval for the proportion of graduates who found a job within one year of completing their undergraduate degree at this university, and interpret it in the context of the data.
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What does “95% confidence” mean?
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Now calculate a 99% confidence interval for the same parameter and interpret it in the context of the data.
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Compare the widths of the 95% and 99% confidence intervals. Which one is wider? Explain.