Solved: Expand Your Knowledge: Software Approximation for

Chapter , Problem 21

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Expand Your Knowledge: Software Approximation for Degrees of Freedom Given x1 and x2 distributions that are normal or approximately normal with unknown s1 and s2, the value of t corresponding to has a distribution that is approximated by a Students t distribution. We use the convention that the degrees of freedom is approximately the smaller of n1 1 and n2 1. However, a more accurate estimate for the appropriate degrees of freedom is given by Satterthwaites formula: 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 13, we tested whether the population average crime rate m2 in the Rocky Mountain region is higher than that in New England, m1. The data were n1 10, and Use Satterthwaites formula to compute the degrees of freedom for the Students t distribution.