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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
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Bar Graphs and Pareto Charts
(0)

Pie Charts
(0)

Frequency Polygons
(0)

Dot Plots
(0)

Stemplots (Stem-and-Leaf Plots)
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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 Test

14. ANOVA

Multiple Comparisons: Tukey Test: Videos & Practice Problems

Learn Concepts Practice Worksheet

Back to all problems

7 of 0

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Problem 7Multiple Choice

An agricultural trial compares three fertilizer formulas (X, Y, Z) with n = 8 plots per formula. The ANOVA rejects the overall null. The instructor provides q_crit = 3.40 for alpha = 0.05, k = 3 groups, and df = 21. Use MSE = 9.0 and group means X = 12, Y = 15, Z = 20. Compute all three pairwise q statistics and state which pairwise comparisons are significant at alpha = 0.05.

q_XY ≈ 2.83 (not significant), q_YZ ≈ 4.72 (significant), q_XZ ≈ 7.55 (significant); conclude Y vs Z and X vs Z differ.

None of the q statistics exceed q_crit = 3.40, so fail to reject all pairwise null hypotheses and conclude the fertilizers perform equivalently across plots.

q_XY ≈ 3.40 (borderline), q_YZ ≈ 4.00 (significant), q_XZ ≈ 6.00 (significant); conclude all three are significant at alpha 0.05.

All pairwise q values exceed q_crit = 3.40 because the largest difference is large, therefore X differs from both Y and Z and Y differs from Z as well.

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