7.4Estimating the Difference in Means of Two Normal Populations 259
the estimator ofσ^2 is thepooled estimator
Sp^2 =
(n−1)S 12 +(m−1)S 22
n+m− 2
and the confidence interval is then based on the statistic
X−Y−(μ 1 −μ 2 )
√
Sp^2
√
1/n+1/m
The 90% confidence interval for the mean difference is (2.4971, 11.9315)
Confidence Interval: Unknown But Equal Variances
Start
Quit
(a)
Clear List 2
Clear List 1
One-Sided
Two-Sided
Upper
Lower
Enter the value of a:
(0 < a < 1)
.1
Data value = 135
Data value = 142
152
144
132
142
150
154
136
142
List 1 Sample size = 12
Add This Point To List 1
Remove Selected Point From List 1
List 2 Sample size = 14 134
130
146
128
131
137
135
Add This Point To List 2
Remove Selected Point From List 2
FIGURE 7.5 (a) Two-sided and (b) upper 90 percent confidence intervals for Example 7.4b.