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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. Failure Type
9-66. Patients in a hospital are classified as surgical or med- Mounting Position A B C D
ical. A record is kept of the number of times patients require 1 22 46 18 9
nursing service during the night and whether or not these 2 4 17 6 12
patients are on Medicare. The data are presented here:

Would you conclude that the type of failure is independent of the
Patient Category mounting position? Use 0.01. Find the P-value for this test.
Medicare Surgical Medical 9-70. A random sample of students is asked their opinions on
Yes 46 52 a proposed core curriculum change. The results are as follows.
No 36 43

Opinion
Test the hypothesis (using 0.01) that calls by surgical- Class Favoring Opposing
medical patients are independent of whether the patients are Freshman 120 80
receiving Medicare. Find the P-value for this test. Sophomore 70 130
9-67. Grades in a statistics course and an operations re- Junior 60 70
search course taken simultaneously were as follows for a Senior 40 60
group of students.

Test the hypothesis that opinion on the change is independent of
Operation Research Grade class standing. Use 0.05. What is the P-value for this test?
Statistics Grade A B C Other
Supplemental Exercises
A 25 6 17 13
B 17 16 15 6 9-71. A manufacturer of semiconductor devices takes a ran-
C 18 4 18 10 dom sample of size n of chips and tests them, classifying each
Other 10 8 11 20 chip as defective or nondefective. Let X i 0 if the chip is non-
defective and X i 1 if the chip is defective. The sample frac-
tion defective is
Are the grades in statistics and operations research related? X 1 X 2 p
Use 0.01 in reaching your conclusion. What is the p ˆ n X n
i
P-value for this test?
9-68. An experiment with artillery shells yields the follow- What are the sampling distribution, the sample mean, and
ing data on the characteristics of lateral deflections and sample variance estimates of ˆp when
ranges. Would you conclude that deflection and range are in- (a) The sample size is n 50?
dependent? Use 0.05. What is the P-value for this test? (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
Lateral Deflection the effect of sample size on the variance of the sampling
distribution.
Range (yards) Left Normal Right
9-72. Consider the situation of Exercise 9-76. After collecting
0–1,999 6 14 8
a sample, we are interested in testing H 0 : p 0.10 versus
2,000–5,999 9 11 4
H 1 : p 0.10 with 0.05. For each of the following situa-
6,000–11,999 8 17 6 tions, compute the p-value for this test:
(a) n 50, ˆp 0.095
(b) n 100, ˆp 0.095
9-69. A study is being made of the failures of an electronic (c) n 500, ˆp 0.095
component. There are four types of failures possible and two (d) n 1000, ˆp 0.095
mounting positions for the device. The following data have (e) Comment on the effect of sample size on the observed
been taken: P-value of the test.