Overview
This lecture explains how to use a two-proportion z-interval (2-PropZInt) to assess the effect of mail reminders on voter registration, and how to interpret a confidence interval that is entirely negative.
Study Design & Groups
- Two groups: one received no reminder (group one), the other received a reminder (group two).
- Both groups had 625 potential voters each; group one had 295 register, group two had 350 register.
- Success is defined as registering to vote.
Verifying Conditions
- Random selection of participants was assumed.
- Independence: Each participant either received a reminder or did not.
- Large sample size: Number of successes and failures in each group both > 10.
- Population is large (San Mateo County).
Setting Up the 2-PropZInt
- Identify variables for calculator: X1 = 295, N1 = 625 (no reminder); X2 = 350, N2 = 625 (reminder).
- Plug these values into 2-PropZInt to find the confidence interval.
Interpreting the Confidence Interval
- The resulting confidence interval is from -0.143 to -0.033.
- Both lower and upper bounds are negative, meaning the entire interval is negative.
- If P1 - P2 is negative, then P1 < P2; group two's proportion is higher than group one’s.
- In this context, group two (reminder) has a greater proportion of registered voters.
Writing the Conclusion
- When the entire interval is negative, interpret the difference using positive values for the interval range.
- State: "We are 95% confident that the proportion of voters who will register is between 3% and 14% higher for those sent a reminder compared to those who were not."
Key Terms & Definitions
- 2-PropZInt — a statistical method for calculating confidence intervals between two population proportions.
- Success — in this study, registering to vote.
- Confidence interval — a range that estimates the difference between two population proportions.
- P1, P2 — proportions of registered voters in group one (no reminder) and group two (reminder).
Action Items / Next Steps
- Practice identifying X1, N1, X2, N2 and using them with 2-PropZInt on your calculator.
- Complete template interpretations for different confidence interval scenarios.
- Review Chapter 5 discussion on percentages and intervals.