We are interested in estimating the proportion of graduates at a mid-sized university who found a jobwithin one year of completing their undergraduate degree. suppose we conduct a survey and nd outthat 348 of the 400 randomly sampled graduates found jobs. the graduating class under considerationincluded over 4500 students. chapter7: analysis of categorical data -part 117-8(a)describe the population parameter of interest. what is the value of the point estimate of thisparameter? (b)check if the conditions for constructing a con dence interval based on these data are met.(c)calculate a 95% con dence interval for the proportion of graduates who found a job within oneyear of completing their undergraduate degree at this university, and interpret it in the contextof the data.(d)what does ? 95% con dence? mean? (e)now calculate a 99% con dence interval for the same parameter and interpret it in the context ofthe data.(f)compare the widths of the 95% and 99% con dence intervals. which one is wider? explai

Part A:

From the question, the population parameter of interest is the proportion of graduates at a mid-sized university who found a job within one year of completing their undergraduate degree.

The value of the point estimate of this parameter is given by

Part B:

The conditions that must be met before constructing a confidence interval include:

The sample size is large.



Since, npq > 10, the conditions for constructing confidence interval are met.



Part C:

The 95% confidence interval for the proportion of graduates who found a job within one year of completing their undergraduate degree at this university is given by:



Part D:

We are 95% confident that the proportion of graduates at a mid-sized university who found a job within one year of completing their undergraduate degree is between 0.84 and 0.90



Part E:

The 99% confidence interval for the proportion of graduates who found a job within one year of completing their undergraduate degree at this university is given by:



Part F:

The width of the 95% confidence interval is 0.06 while the width of the 99% confidence inteval is 0.08.

The 99% confidence interval is wider.

The wider the width of a confidence interval, the more confident we are that the required proportion is in the interval.