7.144 Sample size calculation Example 7.13 (page 449) tells us that the mean hei

Question

7.144 Sample size calculation 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 nul 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 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?

Explanation / Answer

2-Sample t Test

Testing mean 1 = mean 2 (versus )
Calculating power for mean 1 = mean 2 + difference
= 0.05 Assumed standard deviation = 3.2

            Sample Target
Difference    Size   Power Actual Power
       0.7     441     0.9      0.900562

sample size required = 441

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