Problem Sets For Lessons
All content copyright J.W. Crawley

NOTE: This version of the material is based on lessons which teach confidence intervals before hypothesis tests.

Lesson 1. Data, Samples, and Populations

 Complete frequency tables: Frequency tables

 Calculate proportions: Proportions
 Convert to percent or decimal form: Conversions
 Calculate probabilities: Probabilities

Lesson 2. Graphical and Numerical Descriptions of Data

 Calculate the median: Median
 Calculate the IQR (and Q1, Q3): IQR
 Calculate the mean and standard deviation: Mean and standard deviation

 Calculate the z score for a given data value: Calculate z score
 Determine the data value that corresponds to a given z score: From z to x

Lesson 3. Association Between Variables

 Calculate and interpret ratio of two means: Ratio of means

 Calculate proportions for contingency tables: Proportions
 Calculate probabilities for contingency tables: Probabilities

 Calculate correlation and regression line: Correlation and regression
 Interpret slope of regression line, and use regression line for predictions: Regression line calculations

Lesson 4. Probability, Probability Distributions, and the Normal Distribution

 Using Table A, part 1: Using Table A
 Using Table A, part 2 (applications): Applications of Table A

 Calculate probabilities for normal distributions: Normal distribution probabilities

 Calculate P-values for normal distributions: Normal distribution P-values

Lesson 6. Introduction to Inferential Statistics: Confidence Intervals

Experiments leading to confidence intervals

 First experiment with dice: Estimate a dice probability, part 1
 Second experiment with dice: Estimate a dice probability, part 2
 First experiment with surveys: Estimate a population proportion, part 1
 Second experiment with surveys: Estimate a population proportion, part 2
 Third experiment with surveys: Estimate a population proportion, part 3

Histograms for distributions of sample proportions

 Sampling from a population with population proportion p: Sampling distribution

Lesson 7. Confidence Intervals for Proportions

Histograms for distributions of sample proportions

 Sampling from a population with population proportion p
  Version 1 (scale of histogram based on the range of data): Sampling distribution version 1
  Version 2 (same scale for all sample sizes): Sampling distribution version 2

Practice with calculations and interpretation

 Proportion confidence intervals, limited to 95% confidence level
   Just the calculations: Confidence interval calculations
   Calculations with conclusions: Confidence intervals with conclusions
   Same as previous, but app does the calculations: Just conclusions
   Multiple-answer interpretation: More interpretation

 Proportion confidence intervals, variety of confidence levels
   Calculations with conclusions: Confidence intervals with conclusions
   Same as previous, but app does the calculations: Just conclusions
   Multiple-answer interpretation: More interpretation

Lesson 8. Hypothesis Tests for Proportions

Experiments leading to hypothesis testing

 First experiment with dice: Keep or discard dice, part 1
 Second experiment with dice: Keep or discard dice, part 2
 Third experiment with dice: Keep or discard dice, part 3
 Fourth experiment with dice: Keep or discard dice, part 4

Histograms for distributions of sample proportions

 Tossing dice, counting 7s
  Version 1 (scale of histogram based on the range of data): Sampling distribution version 1
  Version 2 (same scale for all sample sizes): Sampling distribution version 2

 Tossing dice, counting even rolls
  Version 1 (scale of histogram based on the range of data): Sampling distribution version 1
  Version 2 (same scale for all sample sizes): Sampling distribution version 2

 Sampling from a population with population proportion p
  Version 1 (scale of histogram based on the range of data): Sampling distribution version 1
  Version 2 (same scale for all sample sizes): Sampling distribution version 2

Follow up exercises. Do some calculations and interpretation for dice

  Calculations for testing by counting 7s: Calculations for counting 7s
  Same problems but just the interpretation: Interpretation for counting 7s

  Calculations for testing by counting various results: Calculations, variety of problem types
  Same problems but just the interpretation: Interpretation, variety of problem types

Practice with calculations and interpretation for sampling from a population, two-tail tests

  Just the calculations, no terminology: Proportion HT calculations version 1
  Add choosing hypotheses and interpreting results: Proportion HT calculations version 2
  Same as the previous, but app does the calculations, user does the interpretation: Proportion HT conclusions version 1
  Multiple-answer interpretation: Proportion HT interpretation version 1

Mix of one-tail and two-tail tests

  Calculations and conclusions: Proportion HT calculations version 3
  Same as the previous, but app does the calculations, user does the interpretation: Proportion HT conclusions version 2
  Multiple-answer interpretation: Proportion HT interpretation version 2

Lesson 9. Using Technology

Repeat of Lesson 7 and Lesson 8 exercises, but this time use technology

 Proportion confidence intervals
   Version 1 - limited to 95% confidence intervals: 95% CI for proportions
   Version 2 - variety of confidence levels: Proportion CI

 Proportion hypothesis tests
   Version 1 - two-tail hypothesis tests: Proportion HT calculations (two-tail only)
   Version 2 - mix of one-tail and two-tail tests: Proportion HT calculations

Lesson 10. Inferences for Categorical-Categorical Association

 Carry out chi-square test, version 1: Chi-square calculations
 Same as previous, but explanation of calculations includes more details: Chi-square calculations

 Write hypothesis and conclusion for a chi-square test: Chi-square questions
 Same as previous, but explanation of calculations includes more details: Chi-square questions

 Multiple-answer interpretation for Chi-Square hypothesis tests: Chi-Square interpretation

 Calculate two-proportion confidence interval and answer question about interpretation: Two-proportion CI
 Same as the previous, but app does the calculations, user does the interpretation: Two-proportion CI - conclusions

 Multiple-answer interpretation for two-proportion confidence intervals: Two-proportion CI interpretation

Lesson 11. Hypothesis Tests and Confidence Intervals for Means

 Calculate mean confidence interval, including conclusions: Mean confidence intervals
 Same as the previous, but app does the calculations, user does the interpretation: Mean CI interpretation

 Multiple-answer interpretation for mean confidence intervals: More mean CI interpretation

 Carry out mean hypothesis tests, including hypotheses and conclusions: Mean hypothesis tests
 Same as the previous, but app does the calculations, user does the interpretation: Mean HT interpretation

 Multiple-answer interpretation for mean hypothesis tests: More mean HT interpretation

Lesson 12. Inferences for Categorical-Numerical Association

 Carry out ANOVA tests, including hypotheses and conclusions: ANOVA calculations
 Same as the previous, but app does the calculations, user does the interpretation: ANOVA questions

 Multiple-answer interpretation for ANOVA tests: ANOVA analysis

 Calculate two-sample mean interval and answer question about interpretation: Two-mean CI
 Same as the previous, but app does the calculations, user does the interpretation: Two-mean CI - conclusions

 Multiple-answer interpretation for two-sample mean confidence intervals: Two-mean CI interpretation