Overview
This lecture covers how to use a graphing calculator to compute and interpret a confidence interval for the difference between two population proportions.
Finding the Confidence Interval with a Calculator
- Use your calculator instead of hand calculations to find the confidence interval for two population proportions.
- On the calculator, navigate to "Stat" → "Tests" → select option "B: 2-PropZInt" for two-proportion z-interval.
- "2-PropZInt" calculates a confidence interval for the difference between two population proportions.
- Input required values: X1 (successes in group 1), N1 (sample size for group 1), X2 (successes in group 2), N2 (sample size for group 2), and the confidence level (e.g., 0.95).
- Example values: X1 = 1,410; N1 = 3,000; X2 = 930; N2 = 3,000; confidence level = 0.95.
- After calculation, the output is a confidence interval (e.g., 0.1357 to 0.1843).
Interpreting the Confidence Interval
- The interval represents possible values for the difference (P1 - P2), not the proportions themselves.
- Determine if the interval is entirely positive, entirely negative, or contains zero.
- If both bounds are positive, the entire interval is positive.
- A positive interval means P1 - P2 is greater than zero, indicating P1 is larger than P2.
- Algebraically, if P1 - P2 > 0, then P1 > P2; group one's proportion is significantly larger.
- For interpretation: "We are 95% confident that the difference in proportions is between 13.6% and 18.4%, and group one has the higher proportion."
Key Terms & Definitions
- 2-PropZInt — Calculator function for two-proportion z-interval (difference between proportions).
- X1, X2 — Number of successes in group 1 and group 2.
- N1, N2 — Sample sizes for group 1 and group 2.
- Confidence Interval — Range of values within which the true difference between proportions is expected to lie with a specified confidence level.
- P1, P2 — Proportion of successes in group 1 (P1) and group 2 (P2).
Action Items / Next Steps
- Practice using "2-PropZInt" with provided data.
- Prepare to interpret intervals in terms of direction (positive/negative/contains zero) and group comparison.
- Review examples of interpreting confidence intervals for proportion differences.