Chapter 9: Introduction to Hypothesis Testing

418 CHAPTER 9 • INTRODUCTION TO HYPOTHESIS TESTING
hypothesis. Use 0.05 and a standard deviation
of 50.
9-62. The union negotiations between labor and
management at the Stone Container paper mill in
Minnesota hit a snag when management asked
labor to take a cut in health insurance coverage.
As part of its justification, management claimed
that the average amount of insurance claims filed
by union employees did not exceed $250 per
employee. The union’s chief negotiator requested
that a sample of 100 employees’ records be
selected and that this claim be tested statistically.
The claim would be accepted if the sample data did
not strongly suggest otherwise. The significance
level for the test was set at 0.10.
a. State the null and alternative hypotheses.
b. Before the sample was selected, the negotiator
was interested in knowing the power of the null
hypothesis if the mean amount of insurance
claims were $260. (Assume the standard deviation
in claims is $70.00, as determined in a similar
study at another plant location.) Calculate
this probability for the negotiator.
c. Referring to part b, how would the power of the
test change if 0.05 is used?
d. Suppose alpha is left at 0.10, but the standard
deviation of the population is $50.00 rather than
$70.00. What will be the power of the test? State
the generalization that explains the relationship
between the answers to part b and d.
e. Referring to part d, based on the probability
computed, if you were the negotiator, would
you be satisfied with the sampling plan in
this situation? Explain why or why not.
What steps could be taken to improve the
sampling plan?
9-63. BusinessWeek indicated in an article (Robert
Barker, “Brew at Bargain Prices,” August 8, 2005)
that per capita U. S. beer consumption in 2004 was
21.6 gallons. A survey is designed to determine if
the per capita consumption has changed in the current
year. A hypothesis test is to be conducted
using a sample size of 1,500, a significance level of
0.01, and a standard deviation of 40. Determine the
probability that the test will be able to correctly
detect that the per capita consumption has changed
if it has declined by 10%.
9-64. Runzheimer International, a management consulting
firm specializing in transportation reimbursement,
released the results of a survey on July 28,
2005. It indicated that it costs more to own a car in
Detroit, an amazing $11,844 a year for a mid-sized
sedan, than in any other city in the country. The
survey revealed that insurance, at $5,162 annually
for liability, collision, and comprehensive coverage,
is the biggest single reason that maintaining a car
in the Motor City is so expensive. A sample size
of 100 car owners in Los Angeles was used
to determine if the cost of owning a car was
more than 10% less than in Detroit. A hypothesis
test with a significance level of 0.01 and a
standard deviation of $750 is used. Determine the
probability that the test will conclude that the cost
of owning a car in Los Angeles is not more than
10% less than in Detroit when in fact the average
cost is $10,361.
Computer Database Exercises
9-65. In an article in BusinessWeek (“Living on the
Edge at American Apparel,” June 27, 2005),
Dov Chaney, the CEO of American Apparel,
indicated that the apparel store industry’s average
sales were $1,800/7 ( $257.14) a square foot.
A hypothesis test was requested to determine if
the data supported the statement made by the
American Apparel CEO using an 0.05 and
the sample size of 41. Produce the probability
that the data will indicate that American Apparel
stores produce an average of seven times the
apparel industry average when in fact they only
produce an average six times the apparel industry
average with a standard deviation of 100. The
CD-ROM file called Apparel contains data for a
random sample of several competitors’ sales per
square foot. Use 0.05.
9-66. USA Today reports (Gary Stoller, “Hotel bill mistakes
mean many pay too much,” July 12, 2005)
that George Hansen, CEO of Wichita-based
Corporate Lodging Consultants, conducted a recent
review of hotel bills over a 12-month period. The
review indicated that, on average, errors in hotel
bills resulted in overpayment of $11.35 per night.
To determine if such mistakes are being made at a
major hotel chain, the CEO might direct a survey
yielding the following data:
9.99 9.87 11.53 12.40 12.36 11.68 12.52 9.34 13.13 10.78
9.76 10.88 10.61 10.29 10.23 9.29 8.82 8.70 8.22 11.01
12.40 9.55 11.30 10.21 8.19 10.56 8.49 7.99 8.03 10.53
The CD-ROM file OverPay contains this data.
a. Conduct a hypothesis test with 0.05 to
determine if the average overpayment is smaller
than that indicated by Corporate Lodging
Consultants.
b. If the actual average overpayment at the hotel
chain was $11 with an actual standard deviation
of $1.50, determine the probability that the
hypothesis test would correctly indicate that the
actual average is less than $11.35.