Section 8.1 Summary

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  1. Using a single statistic only, such as , to estimate a population parameter is called point estimation. The value of the statistic is called the point estimate.

  2. A confidence interval estimate of a parameter consists of an interval of numbers generated by a point estimate, together with an associated confidence level specifying the probability that the interval contains the parameter. The confidence interval for is given by the interval

    where is the confidence level. If is not known, then the interval cannot be used. You may use the following generic interpretation for the confidence intervals that you construct: “We are 90% (or 95%, or 99%, and so on) confident that the population mean _____ lies between _____ (lower bound) and ______ (upper bound).”

  3. The margin of error is a measure of the precision of the confidence interval estimate. For the interval for the mean, the margin of error takes the form

    Usually, our confidence intervals take the form

  4. To use a interval to estimate the population mean to within a margin of error with confidence , the required sample size is given by

    where is associated with the desired confidence level (Table 1), is the desired margin of error, and is the population standard deviation. Round up to the next integer if there is a decimal.