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Confidence Interval for Magnitudes

Given: X ̅ = 97, sx = 16, nx = 64, Y ̅ = 90, sY = 18, nY = 81; assume the samples are independent. Construct a confidence interval of μX - μY according to (a) C = .95 and (b) C = .99

Here are some notes:
Rule for constructing a confidence interval for μX - μY when σx and σy are unknown
(X ̅- Y ̅) ±t_p s_(X ̅-Y ̅ )
tp is the magnitude of t for which the probability is p of obtaining a value so deviant or more so (in either direction)
p = (1 - C) where C is the confidence coefficient
s_(X ̅-Y ̅ ) is the estimate of the standard error of the difference between two means

d= (t_p s_(X ̅-Y ̅ ))/s_av
d is the difference between (X ̅- Y ̅) and the outer limits of the interval estimate, expressed in terms of the number of standard deviations of the variable
s_av is the average of sx and sy ( which is reasonable satisfactory if nx and ny are approximately the same size)


Solution Summary

The confidence intervals for magnitudes are examined. The average confidence interval for the outer limits are determined.