A product developer is interested in reducing the drying time of a primer paint. Two formulations of the paint are tested: formulation 1 is the standard chemistry, and formulation2 has a new drying ingredient that should reduce drying time. From experience it is known that the standard deviation of drying time is 9 minutes, and this variability should be the same for the new formulation. The new formulation will be considered a success if its average drying time is 10 minutes less that the drying time for the existing formulation. If we would like to be able to detect such a difference with probability at least 0.85, and with a Type I error rate of 0.05, what sample size do we need for each of our formulation?
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The solution discusses the design and analysis of an experiment.