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 ? = 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

Answer to the question)
The formula of sample size is

n = (z*S/E)^2

we got e = 0.4

z = 1.645 for 90% confidence

S = 2.5

.

On plugging these values we get

n = (1.645 * 2.5 / 0.4)^2

n = 105.7041 ~ 106

.

Thus we need to consider 106 boys and 106 girls

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