We want to compare the average heights of two types of tree

. We want to compare the average heights of two types of trees. A pilot study shows that the heights of tree type # 1 are between 31 and 50 foot and those of tree type #2 are between 22 and 35 foot. If equal sample sizes are desired, how large should they be in order to ensure that our estimate of the difference in the tree average heights is within 2 foot of the true value with 95% certainty?

Solution

n1 = n2 = n...

mean for average height of tree type 1 = x1-bar and of type-2 = x2-bar......
since , the ranges of heights are given! we have to estimate : s.d( type1) = (50-31) /4 =4.75
and sd( type 2 ) = (35-22) /4 = 3.25..
expected margin of error = 2 ( given)

so , 2 = ( z*score) * sqrt [ ( 4.75)^2 / n + ( 3.25)^2 / n ]
or, 2 = 1.96 * sqrt [ 33.125 / n ]
or, n = 31.81 or, approximately = 32...