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9: Confidence Intervals

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    In this chapter, you will learn to construct and interpret confidence intervals. You will also learn a new distribution, the Student's-t, and how it is used with these intervals. Throughout the chapter, it is important to keep in mind that the confidence interval is a random variable. It is the population parameter that is fixed.

    • 9.0: Prelude to Confidence Intervals
      In this chapter, you will learn to construct and interpret confidence intervals. You will also learn a new distribution, the Student's-t, and how it is used with these intervals. Throughout the chapter, it is important to keep in mind that the confidence interval is a random variable. It is the population parameter that is fixed.
    • 9.1: A Single Population Mean using the Normal Distribution
      A confidence interval for a population mean with a known standard deviation is based on the fact that the sample means follow an approximately normal distribution.
    • 9.2: A Single Population Mean using the Student t-Distribution
      We rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation ss as an estimate for σσ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
    • 9.3: A Population Proportion
      The procedure to find the confidence interval, the sample size, the error bound, and the confidence level for a proportion is similar to that for the population mean, but the formulas are different.
    • 9.S: Confidence Intervals (Summary)
      In this module, we learned how to calculate the confidence interval for a single population mean where the population standard deviation is known.

    This page titled 9: Confidence Intervals was last modified on Wed, 05 Jun 2024 06:32:04 GMT and is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform.