Unit 9: Testing Claims About Proportions

The Logic of Significance: That we assume the Null Hypothesis is true and look for evidence to support the Alternative Hypothesis.

The Definition of a P-value: The probability of getting a sample result as extreme as, or more extreme than, the one observed, given that the null hypothesis is true.

The Error Types: Type I Error: Rejecting a true H0 (a "False Alarm").Type II Error: Failing to reject a false H0 (a "Missed Opportunity").

The Power of a Test: The probability that a test will correctly reject a false null hypothesis.

The Purpose of Pooling: Why we combine data from two samples to estimate a single "pooled proportion" when the null hypothesis assumes the two groups are equal.

Formulate Hypotheses: Write clear H0 and Ha statements using correct parameter notation.

Verify Conditions: Check the Random, 10%, and Large Counts conditions. (Note: In 9.2 and 9.3, Large Counts are checked using the null or pooled proportions, not the sample data).

Calculate Test Statistics: Compute z-scores that measure how many standard deviations the observed sample proportion falls from the hypothesized value.

Determine P-values: Use technology (like 1-PropZTest or 2-PropZTest) or Table A to find the area under the Normal curve corresponding to the z-statistic.

The 4-Step Inference Process: Students will complete a full State-Plan-Do-Conclude cycle for both one-sample and two-sample scenarios.

Standardized Conclusions: Students will provide a two-part conclusion:

• Compare: "Since the P-value is [less/greater] than alpha..."
• Decide: "...we [reject/fail to reject] H0. We [have/do not have] convincing evidence for Ha."

Consequence Analysis: Students will be able to explain the real-world impact of a Type I or Type II error in the context of the problem (e.g., "A Type I error would mean the company spends money on a new ad campaign that doesn't actually work").

Connection to Confidence Intervals: Students will demonstrate an understanding that a two-sided test at alpha = 0.05 will yield the same conclusion as a 95% confidence interval.