Suppose the true mean increase in BMI among heavy-smoking women 6 years after quitting is 3.0 kg/m²with a standard deviation of 2.5 kg/m². The comparable true mean increase in BMI among never-smoking women over 6 years is 1.5 kg/m²with a standard deviation of 2.0 kg/m². How much power does the study in Problem 8.132 have of finding a significant difference if a two-sided test is used with a 5% significance level? 

One issue is that there has been a secular change in weight in society. For this purpose, a control group of 50- to 54-year-old never-having-smoked women were also identified and their BMI was reported at baseline (ages 50ˆ’54) and 6 years later at a follow-up visit. The results are given in columns 2 and 3 of Table 8.32.

Table 8.32: BMI change in 50- to 54-year-old women over a 6-year period

 

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Never-Having-Smoked women Heavy-smoking women (21 pk/day) BMI 6 years after quitting smoking BMI at 6-year follow-up BMI at basoline BMI at baseline ID ID 26.5 29.3 11 25.6 31.1 33.8 32.9 12 24.4 27.6 3 27.6 25.5 13 31.0 36.6 24.4 28.3 14 20.4 20.8 23.3 21.6 15 22.3 23.2 37.1 23.8 6. 32.3 16 22.2 31.9 35.4 17 20.8 26.1 24.8 23.5 23.0 18 31.0 31.2 30.4 19 26.6 29.2 24.0 10 36.3 37.1 20 23.0 Mean 28.9 30.4 24.0 27.3 sd 4.9 5.1 3.1 4.7 10 10 10 10 in