Expand Your Knowledge: Pooled Two-

Sample Procedures Under the condition that both populations have equal standard deviations

(s1 5s2 ), we can pool the standard deviations and use a Student’s t distribution with degrees of freedom

d. f . 5n1 1n2 2 2 to find the margin of error of a c confidence interval for m1 2m2. This technique demonstrates another commonly used method of computing confidence intervals for m1 2m2.

(a) There are many situations in which we want to compare means from populations having standard deviations that are equal. The pooled standard deviation method applies even if the standard deviations are known to be only approximately equal.
(See Section 10.4 for methods to test that s1 5s2.)
Consider Problem 26 regarding weights of gray wolves in two regions. Notice that s1 5 8.32 pounds and s2 5 8.87 pounds are fairly close. Use the method of pooled standard deviation to find an 85%
confidence interval for the difference in population mean weights of gray wolves in the Chihuahua region compared with those in the Durango region.

(b) Compare the confidence interval computed in part

(a) with that computed in Problem 26. Which method has the larger degrees of freedom? Which method has the longer confidence interval?

AppendixLO1