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 x1 2x2 has a distribution that is approximated by a Student’s t distribution. We use the convention that the degrees of freedom are approximately the smaller of n1 21 and n2 21. However, a more accurate estimate for the appropriate degrees of freedom is given by Satterthwaite’s 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) Use the data of Problem 17 (weights of pro football and pro basketball players) to compute

d. f . using the formula. Compare the result to 36, the value generated by Minitab. Did Minitab truncate?

(b) Compute a 99% confidence interval using

d. f . (Using Table 6 requires using

d. f . 5 35.) Compare this confidence interval to the one you computed in Problem 17. Which

d. f . gives the longer interval?

AppendixLO1

d.f. 1 n 2 + $2 n 1 S