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← Margin of Error - Intro to Inferential Statistics

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Showing Revision 6 created 08/27/2017 by Dejan Trajkovic.

  1. Now, we have our general form of the confidence interval. So, for some y
  2. percent confidence interval, this could be 95%, 99%, anything really. Usually,
  3. it's somewhere in the 90s. Then, the lower bound of the confidence interval is
  4. the sample mean minus the number of standard deviations away from the mean.
  5. Where this z value is the number of standard deviations and sigma divided by
  6. the square root of n is the standard deviation of the sampling distributions.
  7. And then, on the upper bound, we just add the number of standard deviations
  8. away that we want. If we have a 95% confidence interval, we'll have less
  9. standard deviations away than we will for a 98% confidence interval. Remember
  10. that we get this z-value from the z-table. So, if this is a 98% confidence
  11. interval let's say, then we'll have 1% in the tails. And then, we'd look for
  12. the z-score for which 1% is less in a standard normal distribution. The
  13. distance that we go away from x-bar, on either side, is the margin of error.
  14. And as you can see, that's equal to z times sigma divided by root n. And
  15. that's half the width of the confidence interval.