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 \({{ params.description.num1 }}\) of the \({{ params.description.num2 }}\) randomly sampled graduates found jobs. The graduating class under consideration included over \({{ params.description.num3 }}\) students.

Part 1: (a)#

Select the population parameter of interest.

Answer Section#

  • Proportion of graduates from this university who found a job within one month of graduating.

  • Average GPA of graduates from this university within one year of graduating.

  • Total number of faculty members at this university.

  • Proportion of graduates from this university who found a job within one year of graduating.

Part 1: (b)#

What is the value of the point estimate of this parameter?

Answer Section#

Please enter in a numeric value

Part 2#

Check if the conditions for constructing a confidence interval based on these data are met.

Answer Section#

  • This is not a random sample, so the observations are not independent.

  • The success-failure condition is not satisfied: 365 successes, 113 failures, both below 10.

  • The success-failure condition is satisfied: 365 successes, 113 failures, both well above 10.

  • This is a random sample, so the observations are independent.

Part 3: (a)#

Calculate the lower bound of the \({{ params.num_part4.num1 }}\)% confidence interval for the proportion of graduates who found a job within one year of completing their undergraduate degree at this university.

Answer Section#

Please enter in a numeric value

Part 3: (b)#

Calculate the upper bound of the \({{ params.num_part4.num1 }}\)% confidence interval for the proportion of graduates who found a job within one year of completing their undergraduate degree at this university.

Answer Section#

Please enter in a numeric value

Part 3: (c)#

In one sentence interpret this interval in context.

Answer Section#

  • We are \(95\)% confident that only [lower bound]% to [upper bound]% of graduates from this university were employed within six months of finishing their undergraduate degree.

  • We are \(95\)% confident that nearly [lower bound]% to [upper bound]% of graduates from this university didn’t manage to find a job within one year of completing their undergraduate degree.

  • We are \(95\)% confident that about [lower bound]% to [upper bound]% of graduates from this university secured employment within five years of completing their undergraduate degree.

  • We are \(95%\)% confident that approximately [lower bound]% to [upper bound]% of graduates from this university found a job within one year of completing their undergraduate degree.

Part 4#

What does “95% confidence” mean?

Answer Section#

  • 95% confidence means that if we repeated this survey 100 times, 95 of the results would fall within this interval.

  • 95% confidence means that 95% of the graduates found jobs within one year of completing their undergraduate degree.

  • 95% confidence means that the survey was conducted with 95% accuracy.

  • 95% of such random samples would produce a 95% confidence interval that includes the true proportion of students at this university who found a job within one year of graduating from college.

Part 5: (a)#

Calculate the lower bound of the \({{ params.part8.num1 }}\)% confidence interval for the same parameter.

Answer Section#

Please enter in a numeric value in.

Part 5: (b)#

Calculate the upper bound of the \({{ params.part8.num1 }}\)% confidence interval for the same parameter.

Answer Section#

Please enter in a numeric value in.

Part 6#

Compare the widths of the 95% and 99% confidence intervals. Is the 99% confidence interval wider or narrower than the 95% confidence interval? (You can answer this question without having to actually calculate the confidence interval).

Answer Section#

Attribution#

Problem is from the OpenIntro Statistics textbook, licensed under the CC-BY 4.0 license.
Image representing the Creative Commons 4.0 BY license.