Pretend that you want to conduct a cross-sectional study to estimate the mean difference in BMI between people who live in the south and people who live in the west. You know that you want alpha to be 0.05 and will conduct an independent sample (2-sample) t-test. Based on the literature you believe that the mean in the south will be 25.0 and the mean in the west will be 26.0 and that the pooled standard deviation is 1.0.You want to sample an equal number of people in the 2 groups. Beta is 0.10.

	South	West
Sample size (n)	75	83
Mean BMI	27.0	29.0
Pooled standard deviation	3.0

What is the necessary sample size? Repeat this calculation for differences in the means between 0.2 and 0.9 in increments of 0.1