Overview
This lecture introduces hypothesis testing, focusing on how to identify claims and formulate null and alternative hypotheses.
Introduction to Hypothesis Testing
- Hypothesis testing is a procedure to test claims or statements about a population.
- It evaluates how much evidence exists for or against the claim.
- The process involves several steps, which will be taught gradually.
Identifying the Claim
- Always start hypothesis testing by determining the claim made about the population.
- The claim reflects what someone thinks is true about the population.
- Carefully read all information to correctly identify the claim (e.g., "now we think it’s higher" suggests a claim of increase).
Writing the Claim Mathematically
- For population proportion (percentage), use the symbol π or P; for mean, use the Greek letter μ (mu).
- Always write the population parameter (π or μ) on the left and the value on the right (e.g., π > 0.04).
- Use ">" for higher/increase, "<" for lower/decrease, and "=" for statements of equality.
Claim Examples
- If side effects percentage was 4% and now it’s believed to be higher, the claim is π > 0.04.
- If evidence suggests average body temperature is lower than 98.6, claim is μ < 98.6.
- If stated as “average is 100,” claim is μ = 100.
Null and Alternative Hypotheses
- The null hypothesis (H₀) is a statement about the population involving equality (e.g., μ = 100).
- The alternative hypothesis (Hₐ) is a statement that does not involve equality (e.g., μ ≠ 100, μ < 98.6, π > 0.04).
- H₀ is denoted as H with subscript 0 (H₀); Hₐ is H with subscript a (Hₐ), sometimes written as H₁.
Formulating Hypotheses
- Opposing views are used to set up null and alternative hypotheses.
- The opposite of "<" is "≥", of ">" is "≤", and of "=" is "≠".
- For one population, usually set H₀ as equality (e.g., μ = value), and Hₐ as the claim without equality.
Key Terms & Definitions
- Hypothesis Test — A procedure for evaluating claims about a population using sample data.
- Claim — The statement or belief to be tested about a population parameter.
- Null Hypothesis (H₀) — The default hypothesis stating no change or effect, involving equality.
- Alternative Hypothesis (Hₐ) — Competing hypothesis indicating change or effect, without equality.
- Population Proportion (π or P) — The percentage of the population with a specific characteristic.
- Population Mean (μ) — The average value for a quantitative population trait.
Action Items / Next Steps
- Practice identifying claims and writing them mathematically.
- Review the symbols π and μ for population parameters.
- Prepare to learn how to test these hypotheses in upcoming lessons.