Given x1 and x2 distributions that are normal or approximately normal with unknown Ï1 and Ï2, the
Question:
where s1, s2, n1, and n2 are the respective sample standard deviations and sample sizes of independent random samples from the x1 and x2 distributions. This is the approximation used by most statistical software. When both n1 and n2 are 5 or larger, it is quite accurate. The degrees of freedom computed from this formula are either truncated or not rounded.
(a) In Problem 15, we tested whether the population average crime rate μ2 in the Rocky Mountain region is higher than that in New England, μ1. The data were n1 = 10, 1 3.51, s1 0.81, n2 = 12, 2 3.87, and s2 0.94. Use Satterthwaites formula to compute the degrees of freedom for the Students t distribution.
(b) When you did Problem 15, you followed the convention that degrees of freedom d.f. = smaller of n1 - 1 and n2 - 1. Compare this d.f. with that found by Satterthwaites formula.
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Understanding Basic Statistics
ISBN: 9781111827021
6th Edition
Authors: Charles Henry Brase, Corrinne Pellillo Brase