Applied Statistics and Probability for Engineers

478 CHAPTER 13 DESIGN AND ANALYSIS OF SINGLE-FACTOR EXPERIMENTS: THE ANALYSIS OF VARIANCE

A 95% CI on the difference in means  3  2 is computed from Equation 13-12 as follows:

or

1.74 3  2 4.40

3 17.0015.67 1 2.086 2 ̨ 121 6.51 2
64

3 y 3 .y 2. t0.025,20 12 MSE n 4

A 100(1) percent confidence interval on the difference in two treatment means

ijis

(13-12)

yi.yj.t 2,a 1 n 12

B

2 MSE

n ijyi.yj.t^ 2,a^1 n^12 B

2 MSE

n

Definition

Equation 13-11 is used to calculate the 95% CIs shown graphically in the Minitab output of

Table 13-5. For example, at 20% hardwood the point estimate of the mean is ,

MSE6.51, and t0.025,202.086, so the 95% CI is

or

It can also be interesting to find confidence intervals on the difference in two treatment means,

say, ij. The point estimator of ijis , and the variance of this estimator is

Now if we use MSEto estimate ^2 ,

has a t-distribution with a(n1) degrees of freedom. Therefore, a CI on ijmay be

based on the t-distribution.

T

Yi.Yj. 1 ij 2

12 MSE n

V 1 Yi.Yj. 2 

^2

n 

^2

n 

2 ^2

n

Yi.Yj.

19.00 psi 4 23.34 psi

3 21.167 1 2.086 2 ̨ 1 6.51
64

3 y 4 .t0.025,20 ̨ 1 MSE n 4

y 4 .21.167

A 100(1) percent confidence interval on the mean of the ith treatment iis

yi.t 2,a 1 n 12 (13-11)

B

MSE

n iyi.t^ 2,a^1 n^12 B

MSE

n

Definition

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