Applied Statistics and Probability for Engineers

9-8 CONTINGENCY TABLE TESTS 323

Test the hypothesis (using   0.05) that breakdowns are

independent of the shift. Find the P-value for this test.

9-66. Patients in a hospital are classified as surgical or med-

ical. A record is kept of the number of times patients require

nursing service during the night and whether or not these

patients are on Medicare. The data are presented here:

Would you conclude that the type of failure is independent of the

mounting position? Use   0.01. Find the P-value for this test.

9-70. A random sample of students is asked their opinions on

a proposed core curriculum change. The results are as follows.

Operation Research Grade

Statistics Grade ABCOther

A 25 6 17 13

B 17 16 15 6

C 18 4 18 10

Other 10 8 11 20

Lateral Deflection

Range (yards) Left Normal Right

0 – 1,999 6 14 8

2,000–5,999 9 11 4

6,000–11,999 8 17 6

Failure Type

Mounting Position ABCD

12246189

2 4 17 6 12

Opinion

Class Favoring Opposing

Freshman 120 80

Sophomore 70 130

Junior 60 70

Senior 40 60

Test the hypothesis (using   0.01) that calls by surgical-

medical patients are independent of whether the patients are

receiving Medicare. Find the P-value for this test.

9-67. Grades in a statistics course and an operations re-

search course taken simultaneously were as follows for a

group of students.

Are the grades in statistics and operations research related?

Use      0.01 in reaching your conclusion. What is the

P-value for this test?

9-68. An experiment with artillery shells yields the follow-

ing data on the characteristics of lateral deflections and

ranges. Would you conclude that deflection and range are in-

dependent? Use   0.05. What is the P-value for this test?

9-69. A study is being made of the failures of an electronic

component. There are four types of failures possible and two

mounting positions for the device. The following data have

been taken:

Test the hypothesis that opinion on the change is independent of

class standing. Use      0.05. What is the P-value for this test?

Supplemental Exercises

9-71. A manufacturer of semiconductor devices takes a ran-

dom sample of size nof chips and tests them, classifying each

chip as defective or nondefective. Let Xi 0 if the chip is non-

defective and Xi 1 if the chip is defective. The sample frac-

tion defective is

What are the sampling distribution, the sample mean, and

sample variance estimates ofpˆwhen

(a) The sample size is n 50?

(b) The sample size is n 80?

(c) The sample size is n 100?

(d) Compare your answers to parts (a)–(c) and comment on

the effect of sample size on the variance of the sampling

distribution.

9-72. Consider the situation of Exercise 9-76. After collecting

a sample, we are interested in testing H 0 : p 0.10 versus

with     0.05. For each of the following situa-

tions, compute the p-value for this test:

(a)n 50,ˆp 0.095

(b)n 100,ˆp 0.095

(c)n 500,p ˆ0.095

(d)n 1000,ˆp 0.095

(e) Comment on the effect of sample size on the observed

P-value of the test.

H 1 : p0.10

pˆi

X 1 X 2 p Xn

n

Patient Category

Medicare Surgical Medical

Ye s 4 6 5 2

No 36 43

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