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.
(a) Describe the population parameter of interest. What is the value of the point estimate of this parameter?
(b) Check if the conditions for constructing a confidence interval based on these data are met.
(c) 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. (d) What does "95% confidence" mean?
(e) Now calculate a 99% confidence interval for the same parameter and interpret it in the context of the data.
(f) Compare the widths of the 95% and 99% confidence intervals. Which one is wider? Explain.