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1. Intro to Stats and Collecting Data(0)

Intro to Stats
(0)

Levels of Measurement
(0)

Intro to Collecting Data
(0)

Sampling Methods
(0)

2. Describing Data with Tables and Graphs(0)

Visualizing Qualitative vs. Quantitative Data
(0)

Frequency Distributions
(0)

Histograms
(0)

Bar Graphs and Pareto Charts
(0)

Pie Charts
(0)

Frequency Polygons
(0)

Dot Plots
(0)

Stemplots (Stem-and-Leaf Plots)
(0)

Time-Series Graph
(0)

3. Describing Data Numerically(0)

Mean
(0)

Median
(0)

Mode
(0)

Standard Deviation
(0)

Interpreting Standard Deviation
(0)

Percentiles & Quartiles
(0)

Boxplots
(0)

4. Probability(0)

Basic Concepts of Probability
(0)

Complements
(0)

Addition Rule
(0)

Multiplication Rule: Independent Events
(0)

Introduction to Contingency Tables
(0)

Multiplication Rule: Dependent Events
(0)

Bayes' Theorem
(0)

Fundamental Counting Principle
(0)

Counting
(0)

5. Binomial Distribution & Discrete Random Variables(0)

Discrete Random Variables
(0)

Binomial Distribution
(0)

Poisson Distribution
(0)

Hypergeometric Distribution
(0)

6. Normal Distribution and Continuous Random Variables(0)

Uniform Distribution
(0)

Standard Normal Distribution
(0)

Non-Standard Normal Distribution
(0)

7. Sampling Distributions & Confidence Intervals: Mean(0)

Sampling Distribution of the Sample Mean and Central Limit Theorem
(0)

Introduction to Confidence Intervals
(0)

Confidence Intervals for Population Mean
(0)

Determining the Minimum Sample Size Required
(0)

8. Sampling Distributions & Confidence Intervals: Proportion(0)

Sampling Distribution of Sample Proportion
(0)

Confidence Intervals for Population Proportion
(0)

Chi Square Distribution
(0)

Confidence Intervals for Population Variance
(0)

9. Hypothesis Testing for One Sample(0)

Steps in Hypothesis Testing
(0)

Performing Hypothesis Tests: Means
(0)

Performing Hypothesis Tests: Proportions
(0)

Performing Hypothesis Tests: Variance
(0)

Critical Values and Rejection Regions
(0)

Link Between Confidence Intervals and Hypothesis Testing
(0)

Type I & Type II Errors
(0)

10. Hypothesis Testing for Two Samples(0)

Two Proportions
(0)

Two Means - Unknown, Unequal Variance
(0)

Two Means - Unknown, Equal Variance
(0)

Two Means - Known Variance
(0)

Two Means - Matched Pairs (Dependent Samples)
(0)

Two Variances and F Distribution
(0)

11. Correlation(0)

Scatterplots & Intro to Correlation
(0)

Correlation Coefficient
(0)

12. Regression(0)

Linear Regression & Least Squares Method
(0)

Residuals
(0)

Coefficient of Determination
(0)

Inferences for Slope
(0)

Prediction Intervals
(0)

Quadratic Regression
(0)

13. Chi-Square Tests & Goodness of Fit(0)

Goodness of Fit Test
(0)

Contingency Tables
(0)

Independence Tests
(0)

Homogeneity Tests
(0)

14. ANOVA(0)

Introduction to ANOVA
(0)

Multiple Comparisons: Tukey Test
(0)

Multiple Comparisons: Tukey-Kramer Test
(0)

Multiple Comparisons: Bonferoni Test
(0)

Two-Way ANOVA
(0)

14. ANOVA

Multiple Comparisons: Tukey-Kramer Test

14. ANOVA

Multiple Comparisons: Tukey-Kramer Test: Videos & Practice Problems

Video Lessons Practice Worksheet

Back to all problems

12 of 0

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Problem 12Multiple Choice

A study with three groups obtained the following Tukey HSD q-values: q₁₂ = 1.95, q₁₃= 4.50, q₂₃ = 2.55, and q_critical = 3.05. For each pairwise comparison, state the null hypotheses, determine which group means differ significantly, and explain what these results imply for follow-up interpretation.

H0_12: μ1 = μ2 (fail to reject); H0_13: μ1 = μ3 (reject); H0_23: μ2 = μ3 (fail to reject). Conclude that group 2 differs from both 1 and 3 because group 1 and 3 differ from each other.

H0_12: μ1 = μ2 (reject); H0_13: μ1 = μ3 (reject); H0_23: μ2 = μ3 (reject). Conclude that all means differ because at least one q was above the critical value.

H0_12: μ1 = μ2 (fail to reject); H0_13: μ1 = μ3 (reject); H0_23: μ2 = μ3 (fail to reject). Conclude that only groups 1 and 3 differ significantly; report that ANOVA rejected overall and Tukey-Kramer pinpoints 1 vs 3 as the differing pair.

H0_12: μ1 = μ2 (fail to reject); H0_13: μ1 = μ3 (reject); H0_23: μ2 = μ3 (fail to reject). Conclude that ANOVA was invalid so no pairwise conclusions are warranted unless p-values are available from software.

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