Overview
This lecture explains when a confidence interval allows for making predictions about an outcome, using a political ballot example where the passing threshold is 50%.
Making Predictions with Confidence Intervals
- You can make a prediction when the entire confidence interval fits within your specified restriction.
- For example, if predicting a ballot will pass requires more than 50% votes, the confidence interval for support must be entirely above 50%.
Political Ballot Example
- A poll of 1,000 likely voters found 515 support a proposition.
- Using 1-PropZInt, the resulting confidence interval for support is approximately 48% to 54%.
- This interval includes possible support levels both below and above 50%.
When Prediction is Not Possible
- If any part of the confidence interval falls outside the required restriction (e.g., less than 50%), you cannot make a definite prediction.
- In the example, since the interval includes values below 50%, you can't be certain the proposition will pass.
- Both scenarios exist: some possible support levels predict passing, others predict failing.
Visual Representation
- A visual (blue/orange/red) illustrates when the interval is fully within or partially outside the restriction.
- Prediction is only possible when the entire interval is within the restriction.
Key Terms & Definitions
- Confidence Interval — a range of values that likely contains the true population parameter.
- Restriction — the condition that must be met for a positive outcome (e.g., over 50% votes).
- 1-PropZInt — calculator/statistical function to compute a confidence interval for one proportion.
Action Items / Next Steps
- Review class notes and visual aids on confidence intervals and prediction criteria.
- Practice with sample problems identifying when predictions can and cannot be made from confidence intervals.