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7: Confidence Interval for One Sample

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    • 7.1: Introduction to Confidence Intervals
      Confidence intervals estimate a population parameter, such as a mean or proportion, based on sample statistics. They provide a range likely to contain the true value with a given confidence level, like 95%. This helps measure reliability and account for sampling variability in conclusions.
    • 7.2: Confidence Interval for the Mean Using z-values
      To compute a confidence interval for the mean using z-values, the population standard deviation must be known, and the sample should be randomly selected. This method estimates the range where the true mean lies with a given confidence level. A minimum sample size is often required to ensure accuracy and reliability.
    • 7.3: Confidence Interval for the Mean Using t-values
      To compute a confidence interval for the mean using t-values, use the sample standard deviation when the population standard deviation is unknown. The t-distribution is wider and accounts for extra uncertainty with small samples. It becomes closer to the normal distribution as the sample size increases.
    • 7.4: Confidence Interval and Sample Size for the Proportion
      To compute a confidence interval for a proportion using z-values, use data from a random sample to estimate the range where the true population proportion lies. This method assumes a large enough sample size to approximate normality. Minimum sample size requirements help ensure the distribution is suitable for z-score calculations.
    • 7.5: Formulas for Chapter 7
      In this section, Chapter 7 formulas are presented. These include confidence intervals for the mean using both z-values and t-values, as well as confidence intervals for population proportions. In addition, the formulas for calculating the minimum required sample size to estimate a population mean or a population proportion are included. These formulas help determine the reliability and accuracy of estimates drawn from sample data and are essential tools in inferential statistics.
    • 7.6: Chapter 7 - Key Terms and Symbols
      In this section, the key terms and symbols for Chapter 7 are displayed to provide easy access to important information related to confidence intervals and estimation.

    This page titled 7: Confidence Interval for One Sample was last modified on Thu, 14 Aug 2025 20:32:26 GMT and is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Toros Berberyan, Tracy Nguyen, and Alfie Swan.