Confidence Interval

Confidence-Interval

  • z-Based Confidence Intervals for a Population Mean: $\sigma$ Known
  • t-Based Confidence Intervals for a Population Mean: $\sigma$ Unknown
  • Confidence Intervals for a Population Proportion
  • Sample size determination

Descriptive Statistics $描述性统计$

The science of describing the important aspects of a set of measurements

  • Collect data e.g. Survey
  • Present data e.g. Tables and graphs
  • Characterize data e.g. Sample mean = $\frac{\Sigma X_i}{n}$

Inferential Statistics

The science of using a sample of measurements to make generalizations about the important aspects of a population of measurements.

  • Estimation e.g.: Estimate the population mean weight using the sample mean weight
  • Hypothesis testing e.g.: Test the claim that the population mean weight is 120 pounds

Estimation

  • Point
    • A point estimate is a single number
  • Interval Estimates
    • a confidence interval provides additional information about variability

Population Parameter Sample Statistic
Mean μ X
Proportion π p

An interval estimate provides more information about a population characteristic than does a point estimate

Such interval estimates are called confidence intervals

Confidence interval

The general formula for all confidence intervals is:

\[Point\ Estimate ± (Critical\ Value)(Standard\ Error)\]

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