Introduction to Probability and Statistics for Engineers and Scientists

7.4Estimating the Difference in Means of Two Normal Populations 255

The 95% confidence interval for the mean is (-19.6056, -6.4897)

Confidence Interval: Two Normal Means, Known Variance

Start

Quit

(a)

Clear List 2

Clear List 1

One-Sided

Two-Sided

Upper

Lower

Enter the value of a:

(0 < a < 1)

0.05

Data value = 62

Data value = 44

34

54

52

37

51

44

35

44

List 1 Sample size = 14

Add This Point To List 1

Remove Selected Point From List 1

List 2 Sample size = 12 66

52

60

44

48

46

70

62

Add This Point To List 2

Remove Selected Point From List 2

40

Population

Variance

of List 1

=

100

Population

Variance

of List 2

=

FIGURE 7.4 (a) Two-sided and (b) lower 95 percent confidence intervals for Example 7.4a.

Let us suppose now that we again desire an interval estimator ofμ 1 −μ 2 but that the
population variancesσ 12 andσ 22 are unknown. In this case, it is natural to try to replace
σ 12 andσ 22 in Equation 7.4.1 by the sample variances

S 12 =

∑n

i= 1

(Xi−X)^2

n− 1

S 22 =

∑m

i= 1

(Yi−Y)^2

m− 1