Confidence Interval on Linear Combination of Means, Independent Groups (2 of 5)

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As an example, consider a hypothetical experiment in which aspirin, Tylenol, and a placebo are tested to see how much pain relief each provides. The amount of pain relief is rated on a five-point scale. Four subjects are tested in each group. The data are shown below:
Aspirin      Tylenol    Placebo
   3            2          2
   5            2          1
   3            4          3
   5            4          2
The problem is to calculate the 95% confidence interval on the difference between the average of the aspirin and Tylenol groups and the placebo. That parameter being estimated is:

where μaspirin is the population mean for aspirin, μTylenol is the population mean for Tylenol, and μplacebo is the population mean for the placebo.

The first step is to find the coefficients (a's) so that

Σaiμi =

where aspirin is Condition 1, Tylenol is Condition 2, and placebo is Condition 3. The solution is: a1= 0.5, a2 = 0.5 and a3= -1. The next step is to compute the 3 sample means.
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