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Review - Sum of Normal Random Variables

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					 Review - Sum of Normal Random Variables

• The weighted sum of two independent normally distributed random
  variables has a normal distribution.

• Example




                              week 11                               1
                 Two Sample Problem
• Sometimes we will be interested in comparing means in two
  independent populations (e.g. mean income for male and females).

• We consider two basic scenarios: populations are normal or
  populations are not normal but the sample sizes are large.




                               week 11                               2
CI for Difference between Two Means – Case I

• Suppose we have two independent large random samples from two
  different populations and we are interested in comparing the means
  of these two populations.

• The confidence interval for the difference between two means in this
  case is…




                                week 11                                3
Example




  week 11   4
  Tests for Difference between Two Means

• Suppose we have two independent large random samples from two
  different populations.

• We are interested in testing H0: μx - μy = δ versus a one sided or a
  two sided alternative…

• Then….




                                 week 11                                 5
Example




  week 11   6
  Minitab CI and Hypothesis Tests for Two Means
• We can use Minitab to construct confidence intervals, conduct
  hypothesis tests, for the difference between two means, two independent
  large iid samples.

• The command in Minitab is
  Stat  basic statistic  2 sample t  complete dialogue box  o.k.

• Note that the data can be in two different columns or in one column
  with another column denoting the population of each observation.

• We can also use Minitab to calculate the power of the two sample
  hypothesis test.

• The command in Minitab is
  Stat  power and sample size  2 sample t  complete dialogue  o.k

                                  week 11                               7

				
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posted:4/9/2010
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