Confidence Intervals(KA/SAP/U11ConfidenceIntervals)

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Unit 11: Confidence Intervals

Master the concepts of confidence intervals with explanations, interactive quizzes, and visualizations.

Introduction to Confidence Intervals

A confidence interval is a range of values, derived from sample data, that is likely to contain the value of an unknown population parameter. It is commonly used in statistics to estimate population parameters (like mean or proportion) and to express the uncertainty of this estimate.

  • Confidence Level: The probability that the interval contains the true parameter (e.g., 95%).
  • Margin of Error: The range above and below the sample statistic.
Visualization: The blue bar is the confidence interval; the red line is the true parameter.

Estimating a Population Proportion

To estimate a population proportion (like the percentage of people who prefer tea over coffee), we use a sample proportion (p̂) and construct a confidence interval around it.

  • Sample Proportion (p̂): The proportion observed in your sample.
  • Standard Error (SE): SE = sqrt[ p̂(1 - p̂) / n ]
  • Confidence Interval: p̂ ± z* × SE
Visualization: Adjust sample size and proportion to see the confidence interval change.

Estimating a Population Mean

To estimate a population mean (like the average height of students), we use the sample mean (x̄) and construct a confidence interval around it.

  • Sample Mean (x̄): The mean observed in your sample.
  • Standard Error (SE): SE = s / sqrt(n)
  • Confidence Interval: x̄ ± t* × SE
Visualization: Adjust sample size, mean, and standard deviation to see the confidence interval change.

Quiz: Test Your Understanding

More Confidence Interval Videos

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