9: Confidence Intervals

Due Week 11 ยท Friday, November 6

Author

Prof. Jack Reilly

Published

Fall 2026

Instructions

Complete the following problems and upload your answers as a PDF file to Blackboard. Upload your .do file as well.

Reminder: the sample command in Stata draws random samples from data in memory, with the number after sample referring to the size of the sample to draw. (So, for instance, the command sample 10 would draw a 10% sample of the dataset.) The dataset protectedlands2022.dta gives the distribution of all protected lands across all countries in the world in the year 2022. For all questions, round to the nearest hundredth.

Questions

  1. Find the mean and standard deviation of protected lands in the population.

  2. Draw a 40% sample of countries from the dataset. What is the mean and standard deviation of this sample?

  3. Calculate 20%, 50%, 80%, 90%, 95%, and 99% confidence intervals for the mean of the sample.

  4. Do each of the confidence intervals contain the true population mean? Are you surprised?

  5. What is the proper interpretation for each of the confidence intervals you calculated above?

NoteAI Use

AI use is allowed on this and every problem set that is graded check/no check in this class. You should disclose any AI use as a matter of standard professional ethics, but you will not be evaluated on whether or not you used AI.

I encourage you, however, to use AI intelligently: use it like a teaching assistant to help you understand the material, not as a bot to automatically solve the problem set for you. Remember that you will not have access to a chatbot during in-class exams, so the problem sets are your chance to practice.