Overview
This lecture covers the process of conducting a hypothesis test for a population proportion using a calculator, focusing on interpreting the P-value and making conclusions.
Performing a 1-PropZTest
- Use the calculator: go to "Stat" > "Test" > "1-PropZTest".
- Enter the null hypothesis proportion (P₀), the number of successes (X), sample size (n), and the alternative hypothesis symbol.
- Example: P₀ = 0.11, X = 43, n = 500, alternative is "<" (less than).
- The test gives a Z-test statistic of 1.72 and a P-value of 0.04.
Comparing P-value and Significance Level
- The significance level (α) is typically set at 0.05.
- Compare the P-value (0.04) to α (0.05).
- If the P-value is smaller than α, reject the null hypothesis.
- Small P-value means the sample result is extreme or surprising under the null hypothesis.
Making Conclusions & Interpreting Results
- When P-value < α: reject the null hypothesis, indicating there is enough evidence for the alternative hypothesis.
- When P-value > α: fail to reject the null, meaning not enough evidence for the alternative.
- In the example, since P-value is 0.04 (< 0.05), we reject the null and conclude there is enough evidence that the proportion has decreased.
Key Terms & Definitions
- Null Hypothesis (H₀) — The statement being tested, usually specifying no change or effect.
- Alternative Hypothesis (H₁ or Ha) — The statement we are seeking evidence for (e.g., the proportion has decreased).
- Significance Level (α) — The threshold for rejecting H₀, commonly set at 0.05.
- P-value — The probability of observing a result as extreme as, or more extreme than, the sample outcome if H₀ is true.
- Z-test Statistic — A standardized value to assess how far the sample proportion is from the hypothesized proportion.
Action Items / Next Steps
- Practice running 1-PropZTest with provided data.
- Review hypothesis test steps and decision rules for interpreting P-values.
- Prepare to apply these steps to similar hypothesis testing problems.