From two normal and independent populations , where the mean of the second popul
ID: 3053756 • Letter: F
Question
From two normal and independent populations , where the mean of the second population is 0.50 less than that of the first, pairs of samples are drawn such that each pair contains one sample from each population. If th e samples from the first population contain 90 variates, and those from th e second 120 variates, and if the st andard deviation of the first population is 10, and that of the second is 8, find the probability that in a pair of samples the difference between the first and the second sample means exceeds 1.00 in absolute value. Please show work
Explanation / Answer
Solution:- The probability that in a pair of samples the difference between the first and the second sample means exceeds 1.00 in absolute value is 0.6515.
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 1.28236
DF = n1 + n2 - 2
D.F = 208
t = [ (x1 - x2) - D ] / SE
t = - 0.39
P(t > - 0.39) = 0.6515
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