length of confidence interval


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PDF Lecture 21: Lengths and expected lengths of confidence intervals

If a confidence interval has the shortest length within a class of confidence intervals then its expected length is also the shortest within the same class 

  • How do you find the length of the confidence interval?

    To obtain this confidence interval, add and subtract the margin of error from the sample mean.
    This result is the upper limit and the lower limit of the confidence interval.

  • What affects the length of a confidence interval?

    As the sample size increases, the length of the interval decreases.
    The moral of the story, then, is to select as large of a sample as you can afford.
    As the confidence level decreases, the length of the interval decreases.

  • The expected length of a confidence interval is shown to equal the integral over false values of the probability each false value is included.
    Thus two desiderata for choosing among confidence procedures lead to the same measure of desirability.

The margin of error m of a confidence interval is defined to be the value added or subtracted from the sample mean which determines the length of the interval: m = z* . Suppose in the example above, the student wishes to have a margin of error equal to 0.5 with 95% confidence.
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