Sample size calculation (optional).

Example 7.13 (page 449) tells us that the mean height of 10-year-old girls is N(56.4, 2.7) and for boys it is N(55.7, 3.8). 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 56.4 − 55.7 = 0.7 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?