Refer to the painkiller study of Exercise 7.5.10. That study included 25 observations in each treatment group and showed an effect size of about 0.5. If this is the true population effect size, what is the (approximate) chance of finding a significant difference between the mean effectiveness of the two drugs in an experiment of this size (i.e., with samples of 25 each)?
Exercise 7.5.10
A pain-killing drug was tested for efficacy in 50 women who were experiencing uterine cramping pain following childbirth. Twenty-five of the women were randomly allocated to receive the drug, and the remaining 25 received a placebo (inert substance). Capsules of drug or placebo were given before breakfast and again at noon. A pain relief score, based on hourly questioning throughout the day, was computed for each woman. The possible pain relief scores ranged from 0 (no relief) to 56 (complete relief for 8 hours). Summary results are shown in the table.

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Pain relief score Treatment Drug Placebo n Mean SD 25 3196 12.05 25 25.32 13.78