Unit 3075: Comprehensive Hypothesis Testing

1. Introduction to Hypothesis Testing

• Definition and purpose of hypothesis testing
• Components: Null hypothesis (H0) and alternative hypothesis (H1)
• Significance levels (α) and p-values
• Steps in conducting a hypothesis test
• Decision rules and interpretation

2. Types of Hypothesis Testing

• Overview of different hypothesis tests
• Z-tests: When to use, assumptions, and interpretation
• T-tests: Types (one-sample, independent samples, paired samples)
• Chi-square tests: Tests for independence and goodness of fit
• ANOVA (Analysis of Variance): Comparing multiple group means
• Regression analysis: Testing coefficients and model fit

3. One-Sample Hypothesis Tests

• Testing a single sample mean
• Testing a single sample proportion
• Calculating test statistics (z and t)
• Finding and interpreting p-values
• Making decisions and conclusions

4. Two-Sample Hypothesis Tests

• Comparing two independent samples
  • Independent samples t-test: assumptions and procedure
• Paired samples t-test: when and how to use
• Constructing and interpreting confidence intervals for differences

5. Chi-Square Test

• Chi-square test for independence
  • Setting up hypotheses
  • Calculating expected frequencies
  • Computing chi-square statistic
  • Degrees of freedom and critical values
• Chi-square goodness of fit test
• Interpretation of results and limitations

6. ANOVA (Analysis of Variance)

• Purpose and when to use ANOVA
• Understanding between-group vs within-group variability
• The F-test: calculation and interpretation
• Assumptions of ANOVA
• Post-hoc tests for multiple comparisons

7. Hypothesis Testing in Regression

• Overview of linear regression analysis
• Testing significance of regression coefficients (t-tests)
• Overall model significance (F-test)
• Assumptions in regression hypothesis testing
• Interpretation of results and diagnostics

8. Type I and Type II Errors

• Definitions and examples
• Consequences of errors in decision-making
• Relationship between α, β, and decision errors
• Strategies to minimize errors

9. Power of a Hypothesis Test

• Definition of statistical power
• Factors affecting power: sample size, effect size, significance level
• Relationship between power and Type II error
• Methods to increase test power

10. Practical Applications of Hypothesis Testing

• Case studies from research, business, and everyday contexts
• Designing hypothesis tests for real-world problems
• Interpreting results to support decision-making
• Common pitfalls and best practices