Confidence Intervals With z

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Confidence Intervals With z

• Statistics 2126

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Introduction

• Last time we talked about hypothesis testing with
  the z statistic
• Just substitute into the formula, look up the p,
  if it is lt .05 we reject H0

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Estimation

• We could also estimate the value of the
  population mean
• Well all we will do in essence is use the data we
  had, and the critical value of z
• The critical value is the value of z where p
  .05
• So for a two tailed hypothesis it is 1.96

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Back to the table

• What value gives you .025 in each tail?
• You could look it up in the entries in the table,
  or use the handy dandy web tool I talked about
  last time

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So now with the old data from last time lets
estimate the mean

• The population mean that is
• 108
• n 9
• ? 15
• z /- 1.96

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Now be careful

• That is the 95 percent confidence interval for
  the estimate of ?
• That does not mean that ? moves around and has a
  95 percent chance of being in that interval
• Rather, it means that there is a 95 percent
  chance that the interval captures the mean

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Two sides of the same coin

• You could use the confidence interval to do the
  hypothesis test.
• Remember our null was that ?100
• Well, the 95 percent confidence interval captures
  100 so the ? of our group, statistically, is no
  different than 100

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Making our estimate more accurate

• How could we make our estimate more precise?
• Increase n
• Decrease z
• If we decrease z we get more false positives
  though right

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So in conclusion

• Confidence intervals allow you to test hypotheses
  and make estimates
• They are affected by the critical value of z and
  the sample size
• We practically can only change the sample size