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 μ_aspirin is the population mean for aspirin, μ_Tylenol is the population mean for Tylenol, and μ_placebo is the population mean for the placebo.

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

Σa_iμ_i =

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.