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Confidence Interval for Magnitudes

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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)

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

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