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Review - Sum of Normal Random Variables

Review - Sum of Normal Random Variables. The weighted sum of two independent normally distributed random variables has a normal distribution. Example. Two Sample Problem. Sometimes we will be interested in comparing means in two

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Review - Sum of Normal Random Variables

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  1. Review - Sum of Normal Random Variables • The weighted sum of two independent normally distributed random variables has a normal distribution. • Example week 11

  2. 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

  3. 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

  4. Example week 11

  5. 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

  6. Example week 11

  7. 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

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