Introduction to Probability and Statistics for Engineers and Scientists

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.