AppliedStatsCourse

Midterm 3 Study Guide

This is meant to be a representative sampling of the key concepts you will need to know, and it is not meant to be exhaustive. You should make sure that you are comfortable with Quizzes 8-11 and Homework Assignments 12-17.

  1. What differentiates random variables from other random phenomena? Give examples of random variables
  2. What conditions must we meet in order to be in the binomial setting?
  3. What is the formula for the binomial distribution?
  4. How do we compute the mean and the standard deviation of a random variable?
  5. How do we compute the mean and standard deviation of the binomial distribution?
  6. What can we say about the mean and standard deviation of a linear transformation of a variable?
  7. What can we say about the mean and standard deviation of a sum of two variables?
  8. What do $X$ and $\hat p$ represent in the binomial setting?
  9. What are the mean and standard deviation of $X$ and $\hat p$ in a binomial setting?
  10. What condition must $n$, $p$ satisfy in order for us to be able to use the normal distribution for the computations in a binomial setting?
  11. What conditions must hold in order for us to be in the IID setting?
  12. What do $\mu$ and $\sigma$ represent in the IID setting?
  13. What are the formulas for the mean and standard deviation of $\bar x$ in the IID setting?
  14. What does the Central Limit Theorem say?
  15. What do we refer to when we talk about the sampling distribution of $\bar x$?
  16. What quantities do we refer to as parameters, and what quantities do we refer to as statistics?
  17. What is the general goal of a confidence interval?
  18. State precisely what the confidence interval for the population mean $\mu$ says, describing all the terms needed along the way.
  19. What are the options we have when we want to reduce the margin of error? What are the tradeoffs?
  20. How do we compute the sample size needed to achieve a specific margin of error?
  21. What is the general idea behind a hypothesis test?
  22. What are the two kinds of conclusions we can get from a hypothesis test?
  23. What errors do we refer to as Type I errors? What about Type II errors?
  24. What three parts of our work in a hypothesis test or confidence interval are affected by the sample size and a change in the sample size?