Applied Statistics and Probability for Engineers

10-4

P-value. If this P-value is sufficiently small, the null hypothesis is rejected. This approach

could also be applied to lower-tailed and two-tailed alternatives.

EXAMPLE S10-1 Insulating cloth used in printed circuit boards is manufactured in large rolls. The manufacturer

is trying to improve the process yield, that is, the number of defect-free rolls produced. A sam-

ple of 10 rolls contains exactly 4 defect-free rolls. From analysis of the defect types, process

engineers suggest several changes in the process. Following implementation of these changes,

another sample of 10 rolls yields 8 defect-free rolls. Do the data support the claim that the new

process is better than the old one, using 

0.10?

To answer this question, we compute the P-value. In our example, n 1 n 2 10, y

8  4 12, and the observed value of x 1 8. The values of x 1 that are more extreme than 8

are 9 and 10. Therefore

The P-value is P.0750.0095.0003.0848. Thus, at the level 

0.10, the null

hypothesis is rejected and we conclude that the engineering changes have improved the

process yield.

This test procedure is sometimes called the Fisher-Irwin test.Because the test depends

on the assumption that X 1 X 2 is fixed at some value, some statisticians argue against use of

the test when X 1 X 2 is not actually fixed. Clearly X 1 X 2 is not fixed by the sampling pro-

cedure in our example. However, because there are no other better competing procedures, the

Fisher-Irwin test is often used whether or not X 1 X 2 is actually fixed in advance.

P 1 X 1 10|12 successes 2 

a

12

10

b a

8

0

b

a

20

10

b

.0003

P 1 X 1 9|12 successes 2 

a

12

9

b a

8

1

b

a

20

10

b

.0095

P 1 X 1 8|12 successes 2 

a

12

8

b a

2

2

b

a

20

10

b

.0750

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