Chapter 9: Introduction to Hypothesis Testing

398 CHAPTER 9 • INTRODUCTION TO HYPOTHESIS TESTING
Business Applications
9-12. A mail-order business prides itself in its ability to
fill customers’ orders in six calendar days or less
on the average. Periodically, the operations manager
selects a random sample of customer orders
and determines the number of days required to fill
the orders. Based upon this sample information, he
decides whether the desired standard is being met.
He will assume that the average number of days to
fill customers’ orders is six or less unless the data
suggest strongly otherwise.
a. Establish the appropriate null and alternative
hypotheses.
b. On one occasion where a sample of 40 customers
was selected, the average number of
days was 6.65, with a sample standard deviation
of 1.5 days. Can the operations manager conclude
that his mail-order business is achieving
its goal? Use a significance level of 0.025 to
answer this question.
c. Calculate the p-value for this test. Conduct the
test using this p-value.
d. The operations manager wishes to monitor the
efficiency of his mail-order service often.
Therefore, he does not wish to repeatedly
calculate z-values to conduct the hypothesis
tests. Obtain the critical value, x, so that the
manager can simply compare the sample mean
to this value to conduct the test. Use x as the
test statistic to conduct the test.
9-13. The National Club Association reported that the
average initiation fee for full membership in U.S.
country clubs was $33,757 in 2004 (Natlclub.org).
Suppose a recent random sample of nine U.S.
country clubs revealed the following initiation
fees:
Full Membership Initiation Fees ($)
34,121 36,472 30,054 36,005 41,295
37,771 31,205 38,299 30,602
Based on the sample information, can you
conclude that initiation fees for U.S. country
club memberships have increased over the 2004
amount? Conduct your test at the α 0.05 level
of significance.
9-14. The director of a state agency believes that the
average starting salary for clerical employees in the
state is less than $30,000 per year. To test her
hypothesis, she has collected a simple random sample
of 100 starting clerical salaries from across the
state and found that the sample mean is $29,750.
a. State the appropriate null and alternative
hypotheses.
b. Assuming the population standard deviation is
known to be $2,500 and the significance level
for the test is to be 0.05, what is the critical
value (stated in dollars)?
c. Referring to your answer in part b, what
conclusion should be reached with respect to
the null hypothesis?
d. Referring to your answer in part c, which of the
two statistical errors might have been made in
this case? Explain.
9-15. The makers of Mini-Oats Cereal have an
automated packaging machine that can be set at
any targeted fill level between 12 and 32 ounces.
Every box of cereal is not expected to contain
exactly the targeted weight, but the average of
all boxes filled should. At the end of every shift
(eight hours), 16 boxes are selected at random
and the mean and standard deviation of the
sample are computed. Based on these sample
results, the production control manager determines
whether the filling machine needs to be readjusted
or whether it remains all right to operate. Use
0.05.
a. Establish the appropriate null and alternative
hypotheses to be tested for boxes that are
supposed to have an average of 24 ounces.
b. At the end of a particular shift during which
the machine was filling 24-ounce boxes of
Mini-Oats, the sample mean of 16 boxes was
24.32 ounces, with a standard deviation of
0.70 ounce. Assist the production control
manager in determining if the machine is
achieving its targeted average.
c. Why do you suppose the production control
manager would prefer to make this hypothesis
test a two-tailed test? Discuss.
d. Conduct the test using a p-value. (Hint: Use
Excel’s TINV function.)
e. Considering the result of the test, which of the
two types of errors in hypothesis testing could
you have made?
9-16. A recent internal report issued by the marketing
manager for a national oil-change franchise indicated
that the mean number of miles between oil
changes for franchise customers is at least 3,600
miles. One Texas franchise owner conducted a
study to determine whether the marketing manager’s
statement was accurate for his franchise’s
customers. He selected a simple random sample of
10 customers and determined the number of miles
each had driven the car between oil changes. The
following sample data were obtained:
3,655 4,204 1,946 2,789 3,555
3,734 3,208 3,311 3,920 3,902