MathIsimple

Hypothesis Testing & Statistical Analysis

Master experimental design principles and hypothesis testing methodology. Learn to design experiments, perform statistical tests, interpret p-values, and understand Type I and Type II errors.

12th Grade
Statistics
~90 min
🎮 Interactive Activity: P-Value Interpreter

Interpret the p-value and decide whether to reject H₀!

Given:

p-value = 0.030
α = 0.05

Decision: Should we reject H₀?

🎮 Interactive Activity: Test Type Classifier

Choose the appropriate statistical test!

Scenario:

Group 1 mean = 75
Group 2 mean = 72
Independent groups

Which test should you use?

1. Hypothesis Testing Framework

Null and Alternative Hypotheses

Hypothesis testing begins with stating null (H₀) and alternative (H₁) hypotheses. The null is the default assumption of no effect; the alternative is what we're testing for.

Example 1: Two-Sided Test

Scenario: Testing if a new drug changes blood pressure

H₀: μ = μ₀ (no change in mean blood pressure)

H₁: μ ≠ μ₀ (mean blood pressure differs)

Test type: Two-sided (two-tailed) test

Example 2: One-Sided Test

Scenario: Testing if a new method increases scores

H₀: μ ≤ μ₀ (no increase or decrease)

H₁: μ > μ₀ (mean increases)

Test type: One-sided (one-tailed) test

Example 3: Test Procedure

Step 1: State H₀ and H₁

Step 2: Choose significance level α (typically 0.05)

Step 3: Calculate test statistic

Step 4: Find p-value or compare to critical value

Step 5: Make decision and interpret in context

2. Type I and Type II Errors
3. P-Values and Statistical Significance
4. Two-Sample t-Test
5. Paired t-Test
6. Two-Proportion z-Test
7. Statistical Power and Sample Size
Frequently Asked Questions

Practice Time!

Practice Quiz
10
Questions
0
Correct
0%
Score
1
What is a Type I error?
2
If p-value = 0.03 and α = 0.05, what should we do?
3
What is the difference between one-sided and two-sided tests?
4
When should you use a paired t-test instead of a two-sample t-test?
5
What does a p-value of 0.001 mean?
6
What is statistical power?
7
For a two-sample t-test comparing means, what are the null and alternative hypotheses?
8
What is the purpose of a control group in an experiment?
9
What does randomization in experimental design accomplish?
10
If a confidence interval for the difference in means is (2.5, 8.3), what can we conclude about H₀: μ₁ = μ₂?