Introduction to Probability and Statistics for Engineers and Scientists

256 Chapter 7: Parameter Estimation

The 95% lower confidence interval for the mean is (-infinity, -7.544)

Confidence Interval: Two Normal Means, Known Variance

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(b)

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

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List 2 Sample size = 12 66

52

60

44

48

46

70

62

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Remove Selected Point From List 2

40

Population

Variance

of List 1

=

100

Population

Variance

of List 2

=

FIGURE 7.4 (continued)

That is, it is natural to base our interval estimate on something like

X−Y−(μ 1 −μ 2 )

√

S 12 /n+S 22 /m

However, to utilize the foregoing to obtain a confidence interval, we need its distribution
and it must not depend on any of the unknown parametersσ 12 andσ 22. Unfortunately, this
distribution is both complicated and does indeed depend on the unknown parametersσ 12
andσ 22. In fact, it is only in the special case whenσ 12 =σ 22 that we will be able to obtain
an interval estimator. So let us suppose that the population variances, though unknown,