Week 3 - Statistics Review

Overview

Welcome to Week 2! Statistical review continues apace.

As before, what you should do this week and the next week depends on your background:

Reading Guide

Chapter 3: Review of Statistics

This is the material you should know, along with supports from Khan Academy ( ). Remember that you don’t need to memorize formulas!

• SW 3.1 Estimation of the population mean
  • Don’t worry too much about BLUE, we’ll come back to it. But make sure you get bias, consistency, and efficiency
  • Discrete random variables
• SW 3.2 Hypothesis tests concerning the population mean
  • Testing hypotheses about a mean
• SW 3.3 Confidence intervals for the population mean
  • Introduction to confidence intervals
  • Confidence intervals for means
  • Note that I expect you can
• SW 3.4 Comparing means from different populations
  • Only the type of two-sample test we’ve been practicing - look at difference between two means where the standard deviation is unknown and you do not assume that they come from the same underlying population distribution. Make sure you can use foruma 3.19 and 3.20
• Skip SW 3.5/3.6
• SW 3.7 Scatterplots, the sample covariance, and the sample correlation
  • Correlation coefficients

Slides

Download this week's slides.

Videos

• Statistics Review Estimators/estimates, confidence intervals, and hypothesis testing

Practice Problems (for class)

You can download them as a word doc here.

1. Consider the random variable X, a person’s height, drawn from a population where the X is distributed normally with mean of 66 and variance of 20.
   1. What is P(X>66.5)?
   2. Suppose we randomly select 125 individuals from that population. What is the probability that the mean height is at least 66.5 inches? Does it matter whether X is distributed normally?
2. For a class project, a student wants to check whether final exam stress raises blood pressure of the students in her class. When they are not under any stress, college students have an average systolic blood pressure of 120mm Hg. For the 50 students in her class, the average blood pressure on the day of the final exam is 125.2 mm Hg with a standard deviation of 12mm Hg.
   1. What is the p-value of her test?
      
   2. What should the student conclude about whether final exam stress is associated with higher blood pressure?
3. Another student wants to check whether final exams raise students’ blood pressure more for chemistry or economics classes. For the 50 students in her economics class, the average blood pressure on the day of the final exam is 125.2 mm Hg with a standard deviation of 12mm Hg. For the 100 students in her chemistry class, the average blood pressure is 120 mm Hg with a standard deviation of 24mm Hg.
   1. Conduct the hypothesis test at the 10% level for whether final exams raise students’ blood pressure more for chemistry or economics students. Set up a null and alternative hypothesis, report your t-statistic, and your conclusion. Use a standard normal distribution table.
      
   2. [Side note] Does this mean that economics exams are more stressful than chemistry? Why or why not?

Solutions here

Video-walkthrough