# Review - Sum of Normal Random Variables by rt3463df

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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

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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.

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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…

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Example

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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….

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Example

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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

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