Hypothesis Testing Summary

Hypothesis Testing Overview

• Purpose: Validate theories/assumptions before action.

• Definition: A hypothesis is an unproven supposition regarding a population parameter.

Hypotheses

• Null Hypothesis (H0): Assumes no change effect; statement of no effect.

• Alternative Hypothesis (HA): Contains proposed population parameter values.

• Assumptions: Start with null hypothesis and test statements about population parameters (e.g., $ext{µ}$, $p$).

Steps in Hypothesis Testing

1. State Hypotheses: H0 as a specific value (e.g., $H0: ext{µ} = 20$) and HA for values not included in H0.

2. Identify Test Statistic Model: Mean or Proportion testing, assume data conditions.

3. Specify Significance Level (α): Probability of falsely rejecting H0 when true (e.g., common levels: 0.05, 0.01).

4. Decision Rule:

   • Reject H0 if p ext{-value} < α.

   • Fail to reject H0 if $p ext{-value} \geq α$.

5. Data Collection: Perform hypothesis test mechanics, often using software.

6. Statistical Decision: Determine whether to reject or not reject H0.

7. Conclusion: State findings in relation to HA and explain in simple terms.

Key Concepts

• P-value: Probability of obtaining observed data under H0.

• Type I Error: Incorrectly reject H0 (false positive).

• Type II Error: Fail to reject H0 when it is false (false negative).

Hypothesis Testing Examples

1. Ski Wax Study:

   • Determine if new wax is worth using based on race times.

2. Acid Rain Study:

   • Assess if proportion of tree damage differs from a known figure (15%).