The mean height of 10-year old girls is N (54.5, 2.7) and for boys it is N (54.1

Question

The mean height of 10-year old girls is N (54.5, 2.7) and for boys it is N (54.1, 2.4). 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 54.5 - 54.1 = 0.4 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 sigma = 2.5, and that we will measure the heights of an equal number of girls and boys. How many of each sex would we need to measure to have a 90% chance of detecting the (true) alternative hypothesis? (Round up to the next whole number.)

Explanation / Answer

here margin of error =E=0.4

for 90% CI, z=1.64485

s1=s2=2.5

hence sample size =n=(s12+s22)*(Z/E)2 =~212

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