XI. Estimation


David M. Lane


  1. Introduction
  2. Degrees of Freedom
  3. Characteristics of Estimators
  4. Confidence Intervals
    1. Introduction
    2. Confidence Interval for the Mean
    3. t distribution
    4. Confidence Interval Simulation
    5. Confidence Interval for the Difference Between Means
    6. Confidence Interval for Pearson's Correlation
    7. Confidence Interval for a Proportion
  5. Exercises

One of the major applications of statistics is estimating population parameters from sample statistics . For example, a poll may seek to estimate the proportion of adult residents of a city that support a proposition to build a new sports stadium. Out of a random sample of 200 people, 106 say they support the proposition. Thus in the sample, 0.53 of the people supported the proposition. This value of 0.53 is called a point estimate of the population proportion. It is called a point estimate because the estimate consists of a single value or point.

The concept of degrees of freedom and its relationship to estimation is discussed in Section B. "Characteristics of Estimators" discusses two important concepts: bias and precision.

Point estimates are usually supplemented by interval estimates called confidence intervals . Confidence intervals are intervals constructed using a method that contains the population parameter a specified proportion of the time. For example, if the pollster used a method that contains the parameter 95% of the time it is used, he or she would arrive at the following 95% confidence interval: 0.46 < π < 0.60. The pollster would then conclude that somewhere between 0.46 and 0.60 of the population supports the proposal. The media usually reports this type of result by saying that 53% favor the proposition with a margin of error of 7%. The sections on confidence interval show how to compute confidence intervals for a variety of parameters.


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