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 σ = 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.)
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 σ = 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.)
Looking for a Similar Assignment? Order now and Get 10% Discount! Use Coupon Code "Newclient"
