Overview
This lecture covers the three main steps for constructing and applying confidence intervals for proportions using a calculator, and how to interpret and use the results in practical situations.
Using the Calculator for Confidence Intervals
- Step one: Confirm you have a good sample before calculation.
- Go to the "Stat" button on your calculator, then navigate to "Test."
- Select "1-PropZInt" (Row A) for confidence intervals for a proportion.
- Enter three values: number of successes ('X'), sample size ('n'), and confidence level (in decimal form).
- All required values come directly from the problem prompt.
- After entering values, press enter to receive the confidence interval (lower and upper bounds).
- Calculators may display the interval in different formats but they represent the same data.
Interpreting Confidence Intervals
- Use a template to interpret results: "We are [confidence level]% confident that between [lower]% and [upper]% of all [population] have [characteristic]."
- Convert interval bounds from decimal to percent by multiplying by 100%.
- Identify and state the population and the success characteristic explicitly in your interpretation.
Application of Confidence Intervals
- Confidence intervals provide a range of plausible values for the population proportion, not a single value.
- To answer practical questions, check if the required value (e.g., 50%) falls within the confidence interval.
- If a required benchmark (like 50%) is not in the interval, it suggests the required condition is not met.
- Applying the interval may inform decisions, such as policy approval or rejection.
Key Terms & Definitions
- 1-PropZInt — Calculator function to find a confidence interval for a population proportion.
- Confidence Interval — A range of values likely containing the true population proportion at a given confidence level.
- Confidence Level — The probability (expressed as a percentage or decimal) that the interval contains the true proportion.
- Number of Successes (X) — Count of individuals in the sample with the characteristic of interest.
- Sample Size (n) — Total number of individuals in the sample.
Action Items / Next Steps
- Practice entering data into "1-PropZInt" on your calculator.
- Review and use the interpretation template for confidence interval reporting.
- Prepare for exam questions covering calculation, interpretation, and real-world application of confidence intervals.