7.146 Sample size calculation. Example 7.10 (page 434) tells us that the mean height of 10-year-old girls is N(56.9, 2.8) and for boys it is N(56.0, 3.5). The null hypothesis that the mean heights of 10-year-old boys and girls are equal is clearly false. The difference in mean heights is 56.9 − 56.0 = 0.9 inch. Small differences such as this can require large sample sizes to detect. To simplify our calculations, let’s assume that the standard deviations are the same—say, σ = 3.2—and that we will measure the heights of an equal number of girls and boys. How many would we need to measure to have a 90% chance of detecting the (true) alternative hypothesis?