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Problems 677
17.1 PROBLEMS 17.1 Test the following sequence of observations by using the runs test and a = .05 to
determine whether the process produced random results.
X X X Y X X Y Y Y X Y X Y X X Y Y Y Y X
17.2 Test the following sequence of observations by using the runs test and a = .05 to
determine whether the process produced random results.
M M N N N N N M M M M M M N N M M M M M N M M
N N N N N N N N N N N N N M M M M M M M M M M M
17.3 A process produced good parts and defective parts. A sample of 60 parts was taken
and inspected. Eight defective parts were found. The sequence of good and defective
parts was analyzed by using Minitab. The output is given here. With a two-tailed test
and a = .05, what conclusions can be reached about the randomness of the sample?
Runs Test: Defects
Runs test for Defects
Runs above and below K = 0.1333
The observed number of runs = 11
The expected number of runs = 14.8667
8 Observations above K, 52 below
P-value = 0.0264
17.4 A Watson Wyatt Worldwide survey showed that 58% of all Hispanic Americans are
satisfied with their salary. Suppose a researcher randomly samples 27 Hispanic
American workers and asks whether they are satisfied with their salary with the
result that 15 say yes. The sequence of Yes and No responses is recorded and tested
for randomness by means of Minitab. The output follows. Using an alpha of .05 and
a two-tailed test, what could you conclude about the randomness of the sample?
Runs Test: Yes/No
Runs test for Yes/No
Runs above and below K = 0.5556
The observed number of runs = 18
The expected number of runs = 14.3333
15 Observations above K, 12 below
P-value = 0.1452
17.5 A Virginia Slims Opinion Poll by Roper Starch found that more than 70% of the
women interviewed believe they have had more opportunity to succeed than their
parents. Suppose a researcher in your state conducts a similar poll and asks the same
question with the result that of 64 women interviewed, 40 believe they have had
more opportunity to succeed than their parents. The sequence of responses to this
question is given below with Y denoting Yes and N denoting No. Use the runs test
and a = .05 to test this sequence and determine whether the responses are random.
Y Y N Y Y N N Y Y Y N N Y N N Y Y Y Y Y N Y Y Y Y N N Y Y N N N Y Y Y N N Y
Y Y Y N Y N Y Y Y N N N Y N N Y Y Y Y Y N N Y Y Y Y
17.6 A survey conducted by the Ethics Resource Center discovered that 35% of all workers
say that coworkers have committed some kind of office theft. Suppose a survey is
conducted in your large company to ask the same question of 13 randomly selected
employees. The results are that five of the sample say coworkers have committed
some kind of office theft and eight say they are not aware of such infractions. The
sequence of responses follows. (Y denotes a Yes answer and N denotes a No answer.)
Use a = .05 to test to determine whether this sequence represents a random sample.
N N N N Y Y Y N N N N Y Y