Pre-Class Assignments, Math 141 Introductory Statistics, Spring 2022
This page uses MathJax to display mathematical notation, so please let me know if any part isn't clear.
Be sure to check back, because this page will be updated often during the semester.
All sections refer to OpenIntro Statistics, Fourth Edition. Be sure to check the typos page for corrections to the text.
Week 2: Due Sunday January 30 @ 11:59 pm
Observational studies vs experiments
Basics of visualizing numerical and categorical variables
To Read
- Section 1.3 Sampling principles and strategies
- Section 1.4 Experiments
- Section 2.1 Examining numerical data (skim 2.1.7 and 2.1.8)
- Section 2.2 Considering categorical data
Pre-Class Questions
- Explain the difference between an observational study and an experiment.
- Consider the bottom histogram shown in Figure 2.9 on page 48. Describe the distribution in a few sentences, including the shape (skewdness and modality), center, variability, and an unusual features.
- Consider Figures 2.20 and 2.21 on page 62.
- What does the value 0.138 in Figure 2.20 represent?
- What does the value 0.802 in Figure 2.21 represent?
- Have you filled out the Background Questionairre yet? (link in onCourse)
Week 3: Due Sunday February 6 @ 11:59 pm
The normal and binomial distributions
To Read
- Section 4.1 Normal distribution
- Section 4.3 Binomial Distribution
Pre-Class Questions
- Which is further from the mean, a data value with a z-score of 1.3 or a data value with a z-score of -1.5? Why?
- In a normal distribution, what percentage of the distribution lies within 1 standard deviation of the mean?
- If a binomial distribution has probability of success p=0.25, is a sample size of n=30 large enough to guarantee that the distribution is approximately normal? What if n=60?
Week 4: Due Sunday February 13 @ 11:59 pm
Sample statistics and the power of the Central Limit Theorem
To Read
- Section 5.1 Point estimates and sampling variability
- Section 5.2 Confidence intervals for a proportion
Pre-Class Questions
- What does each data point in a sampling distribution represent?
- What are the two requirements for the sample proportion \( \hat{p} \) to follow a normal distribution? (You do not need to explain the requirements. We'll talk about them in detail in class.)
- In creating a confidence interval for for a population proportion \( p \), why is it important to know that the sampling distribution for \( \hat{p} \) is normal?
Week 5: Due Sunday February 20 @ 11:59 pm
Understanding what rejecting the null hypothesis tells you, and doesn't tell you
To Read
- 5.3 Hypothesis testing for a proportion
Pre-Class Questions
- What is the null hypothesis H0 of a hypothesis test?
- What is the alternative hypothesis HA of a hypothesis test?
- What does the p-value of a hypothesis test tell you about H0?
Week 6: Due Sunday February 27 @ 11:59 pm
Exam 1
To Read
- Section 6.1 Inference for a single proportion
Read Section 6.1, but no questions this week because of Exam 1.
Week 7: Due Sunday March 6 @ 11:59 pm
Inference for two proportions and for one mean
To Read
- Section 6.2 Difference of two proportions
- Section 7.1 One-sample means with the t-distribution
Pre-Class Questions
- Why do we pool the samples in a two-proportion hypothesis test?
- Why don't we pool the samples in computing a confidence interval for the difference of two proportions?
- Why do we need to use the t-distribution for inferences about means rather than the techniques from Chapter 5?
Week 8: Due Sunday March 20 @ 11:59 pm
Naturally paired data
To Read
- Section 7.2 Paired data
Read Section 7.2, but no questions this week because of Spring Break.
Week 9: Due Sunday March 27 @ 11:59 pm
Inference for two or more means
To Read
- Section 7.3 Difference of two means
- Section 7.5 Comparing many means with ANOVA
Pre-Class Questions
- Explain the difference between a paired t-test and a two sample t-test.
- What is the difference between ANOVA and the two-sample t-tests from Section 7.3?
- Why is a test comparing population means called analysis of variance?
Week 10: Due Sunday April 3 @ 11:59 pm
More with ANOVA and an introduction to linear regression
To Read
- Section 8.1 Fitting a line, residuals, and correlation
Pre-Class Questions
- What is the purpose of regression?
- What does it mean if the residual for a data point (xi, yi) is zero?
- What does the correlation coefficient R measure?
Week 11: Due Sunday April 10 @ 11:59 pm
Exam 2
To Read
- Section 8.2 Least squares regression
Read Section 8.2, but no questions this week because of Exam 2.
Week 12: Due Sunday April 17 @ 11:59 pm
Quantifying uncertainty in regression and regression with multiple inputs
To Read
- Section 8.4 Inference for linear regression
- Section 9.1 Introduction to multiple regression
Pre-Class Questions
- In regression inference, why is the null hypothesis always that slope \(\beta_1=0\)?
- How does multiple regression differ from the linear regression models we discussed in Chapter 8?
Week 13: Due Sunday April 24 @ 11:59 pm
Multiple regression
To Read
- Section 9.2 Model selection
- Section 9.3 Checking model conditions and using graphs
Pre-Class Questions
- What is the advantage of multiple regression over the models from Chapter 8?
- Briefly explain the purpose of backward elimination in refining a multiple regression model.
Week 14: For Sunday May 1
Comparing more than two proportions
To Read
- Section 6.3 Testing for goodness of fit using chi-square
Pre-Class Questions
- What does the chi-square statistic measure? You don't need to give an explicit formula, but explain the idea in your own words in a couple of sentences.