Links
Projects
Project 1: Qualitative Simulation
This StatCrunch coin flip simulation helps students to start thinking inferentially about population proportions. Part 3 requires students to use gender data they collected from their own classes during the first week of class.
Project 2: Two Proportion - Simulation and Randomization
This project uses two of StatCrunch's built-in applets. Simulation can be easily be performed using poker chips of two colors. The randomization applet leads students towards the two-proportion test. In the last two parts students use data they collected by asking male and female students two yes/no questions.
Project 3: Bootstrap - Mean & Median
Students use the bootstrap procedure in StatCrunch to estimate the mean or median of a population based on a sample. Investigation 3 uses data I gathered from my classes concerning the age of my students.
Project 4: Simulation (Mean)
I provide students a set of population data, and they draw samples of size n from it repeatedly. They then develop a type of confidence interval for the mean from those samples, as well as determine whether one sample drawn by hand is unusual or not.
Project 5: Bootstrap - Paired Difference
Students use StatCrunch after learning about the matched-pairs design to bootstrap the mean difference based upon two dependent samples. Students must gather data from two stores (25 items) as part of their investigation of determining which store, if any, is less expensive.
Project 6: Two Mean - Randomization
This project uses StatCrunch's built-in Two-Mean Randomization applet, which leads towards the two-mean (independent samples) test. Students use their own data comparing rankings of Math and English instructors, as well as comparing ratings of instructors at two colleges.
Project 7: Correlation Tests
Students learn the basics of hypothesis testing through correlation. Students gather highway & city MPG for a sample of cars, and investigate the relationship between Overall Quality and Level of Difficulty of their instructors.
Project 8: One Proportion Test - Binomial
Formal introduction of the 5-step hypothesis procedure, including directions for calculating P-values using StatCrunch's binomial calculator.
Examples to use with Project 8
Project 9: Mixed One Proportion Tests
Students use the standard one proportion test if the conditions are met, or use the binomial calculator in StatCrunch to compute P-values of the conditions are not met.
Project 10: Mixed One Proportion and Two Proportion Tests
A mixture of one proportion and two proportion tests. If conditions are not met students turn to the binomial calculator (1 prop) or two proportion randomization test (2 prop) in StatCrunch.
Project 11: One Mean, One Proportion, and Two Proportion Tests and Their Alternatives
Students use alternatives (binomial for 1 prop, randomization for 2 prop, sign test for 1 mean) if the conditions are not met, otherwise they use the standard test.
Project 12: Two Mean Tests and Their Alternative - Mann-Whitney
A mixture of two mean tests and Mann-Whitney tests. If conditions for a two-mean test are not met students turn to the Mann-Whitney nonparametric test.
Project 13: Mixed One Sample and Two Sample Tests and Their Alternatives
Students use alternatives (binomial for 1 prop, randomization for 2 prop, sign test for 1 mean, Wilcoxon Signed Rank test for paired difference, Mann-Whitney test for two mean) if the conditions are not met, otherwise they use the standard test.
Project 14: Mixed Chi-Square and ANOVA Tests
Four examples: goodness-of-fit, independence, ANOVA, and Kruskal-Wallis (nonparametric alternative to ANOVA).
In Class Activites
Sampling Activity
Students earn to use systematic sampling from a known population to estimate a poplation mean and proportion. They also use StatCrunch to generate random numbers to select a sample. Great opportunity for discussion about how samples vary. Finally students draw a random sample from a data set (3 variables) in StatCrunch. I use this as an opportunity to show how easy it is to do calculations and draw graphs in StatCrunch.
Matched-Pairs Activity
Students work in groups to propose how to use a matched-pairs design to investigate 3 scenarios. It provides an opportunity to discuss different strategies in class. I then assign Case 3 (Are the prices lower at store A or store B?) as a data collection exercise to be used later in the semester.
Section 2.1 - Qualitative Graphs
This asks students make pie charts to begin developing inferential intuition. They are also asked to create a frequency distribution, a bar chart, a relative frequency distribution, a relative frequency bar chart, and a pie chart from data.
Section 2.2 - Quantitative Graphs
Three sets of data: stem-and-leaf, frequency distribution, relative frequency distribution, and histogram.
Section 3.1 - Measures of Central Tendency
Find the mean, median, and mode for a set of data. I like to extend problems 1 and 2 by mentioning that I forgot Michael Jordan's starting salary and Mark Zuckerberg's annual income to discuss measures that are resistant.
Chapter 3 Activity - Comparing Two Samples of Quantitative Data
Students analyze two sets of test scores to determine if the tests were of equal difficulty. Great lead-in to Randomization Test for Two Means in StatCrunch.
Section 4.1 - Hypothesis Tests for the Correlation Coefficient
By this point my students are familiar with inferential statistics (simulation, bootstrapping, randomization). I use this as an opportunity to formally introduce the language of hypothesis testing and the 5-step procedure.
Section 4.2 - Linear Regression
Groupwork for finding the least-squares regression equation and using it to make predictions about the dependent variable for a given value of the independent variable.
Sections 5.1-5.3 - Probability Groupwork
Topics include: classical probability, complement rule, addition rule, multiplication.
Section 5.4 - More Probability Groupwork
Topics include: contingency tables, conditional probability, card problems, multiplication, 'at least 1' probabilities.
Power Point - Midterm Review Part 1
I used this file in class to review chapters 1 through 4.
Power Point - Midterm Review Part 2
I used this file in class to review chapters 5 through 7.
In Class Practice Test For The Second Part Of Midterm
I had students work on these problems independently before going over them together.
Confidence Interval for p
Fact sheet for confidence intervals for a population proportion, including conditions, margin of error, upper/lower bounds, interpretation, and StatCrunch steps. Examples show role of confidence level and sample size. Also includes a fact sheet for determining the appropriate sample size to estimate p.
One Proportion Tests
Fact sheet for one proportion tests, including steps and conditions. Three examples: right-tailed, two-tailed, left-tailed.
Alternative Tests for One Proportion
Steps for computing P-value in StatCrunch using the binomial distribution and the Coin-Flip simulator. Three examples: right-tailed, two-tailed, left-tailed.
Two Proportion Test
Fact sheet for the two proportion test, including conditions and summary of how steps differ from one proportion test. Six examples. We work 3 in class, with the remaining 3 assigned as homework.
Two Proportion Test - Resampling
Instructions for building the StatCrunch applet for the randomization test for two proportions and how to determine the P-value. Three examples.
One Mean Test
Fact sheet for one mean test, including identification, differences in steps compared to other tests, conditions, and StatCrunch steps for summary or data. Four examples: 2 with summary statistics and 2 with data.
The Sign Test
General background information for the Sign Test, a nonparametric alternative to the one mean test. StatCrunch directions are given, as well as an explanation of how the steps differ from other tests. Three examples to work in class.
Paired Difference Test
Fact sheet for paired difference test, including conditions, StatCrunch steps, and an explanation of the stes that are different than from other tests. Three examples to work during class.
Wilcoxon Signed Ranks Test
Background information on Wilcoxon Matched-Pairs Signed-Ranks Test. Summary of steps that differ from other tests. There are 4 examples. If the conditions for the paired difference test are met, students use that test. If the conditions fail, students use the Wilcoxon signed-ranks test.
Two Mean Test
Fact sheet for two mean test, including conditions, StatCrunch steps, and explanation of steps that differ from other tests. There are three classroom examples - 2 with summary statistics and 1 with data.
Alternative to Two Mean Test
Background information on Mann-Whitney Test, a nonparametric alternative to the two mean test. Summary of steps that differ from other tests. There are 3 classroom examples for students to work through. If the conditions for the two mean test are met, students use that test. If the conditions fail, students use the Mann-Whitney test.
Alternative Tests - One and Two Sample Tests
This is a summary sheet of various alternative tests. (one and two proportions, one and two means, paired difference)
Goodness of Fit
Fact sheet for Goodness of Fit test, including conditions, differences in steps compared to other tests, and StatCrunch steps. Three classroom examples.
Chi-Square Indepedence Test
Fact sheet for Chi-Square Independence test, including explanation of observed/expected frequencies, conditions, differences in steps compared to other tests, and StatCrunch steps. Four classroom examples.
ANOVA
Fact sheet for (one-way) ANOVA test, including conditions, differences in steps compared to other tests, and StatCrunch steps. Three classroom examples.
Practice Inferential Final
Two part practice final.
Part 1 requires students to perform all calculations. Includes 2 sample size problems, 2 1-sample confidence intervals, several hypothesis tests (1p, 2p, 1 mu, 2 mu, paired difference, goodness of fit, independence, ANOVA), and tests where conditions are not met and students must use an alternative test.
Part 2 contains 8 hypothesis tests where output is provided and students write up the test using a standard procedure. Also includes 1 hypothesis test students have not done before (2 variance test) and 1 journal translation problem (students are given an excerpt from a medical journal and have to translate the results to our standard hypothesis testing procedure).
Practice Final Answer Key
Answer Key to Practice Final
