Key Concepts
- Margin of Error: A range of values within which the true population parameter is expected to fall.
- Computing Plausible Ranges: The true proportion or mean can be anywhere within the given margin of error.
- Distinguishing Estimates from Exact Values: Sample-based estimates provide a range of possible values, not a definitive answer.
Skills Covered
- Calculating confidence intervals by adding and subtracting the margin of error.
- Interpreting plausible ranges.
- Understanding the uncertainty in sample-based predictions.
Example Problems
- A researcher estimates that 40% of students own a pet, with a margin of error of ±5%. Determine the plausible range of actual pet ownership.
- A survey estimates that 30% of employees commute by bike, with a margin of error of ±3%. What does this tell us about the actual proportion of biking commuters?