Stats for Business HOMEWORK 10
(20 exercises for Topic 8: Hypothesis Testing)
DIRECTIONS:
• Use and label the Five Steps of Hypothesis Testing from the Topic 8 Notes.
• For precision, calculate the test statistic (Z or t) in Step 3 without rounding.
There are several ways to do this: The TI graphing calculators let you reference ANS (the
previous answer.) Every calculator has a memory button for which you can Google directions.
Or you can choose to simply “write down all the numbers” if you’d prefer.
• For some exercises you can use either a calculator or MINITAB in the computer lab in 41
SH to calculate x̄ and s, whichever you prefer. (On exams and quizzes, you’ll need to use a
calculator since MINITAB won’t be available.)
• Some textbook exercises listed below have been reordered to provide a better learning experience.
• Exercise 6.39 (page 355)
• Exercise 6.40
• Exercise 6.59
• Exercise 6.60
• Exercise 8.45 (page 471)
Add part (c):
(c) Are the answers to (a) and (b) consistent? Explain in terms of plausibility.
• Exercise 8.98 (page 488)
• Exercise 8.99
(Test using 1% significance.)
Add part (b):
(b) Is the null hypothesis H0 from Exercise 8.98 plausible?
• Exercise 8.101
(Test using 10% significance.)
• Exercise 8.102
(continued)
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• Exercise 8.46
Ignore the textbook’s directions. Answer these questions instead:
(a) Test the claim that a majority of people prefer the taste of fresh-brewed coffee at 5%
significance. (Use and label the Five Steps of Hypothesis Testing.)
(b) Suppose that the sample provides different numbers: Actually only 19 of the 60 subjects prefer instant coffee. Repeat the hypothesis test from part (a).
(c) Briefly explain why the conclusions differ between parts (a) and (b).
(d) Turn to the description of “P -Values” near the end of the Topic 8 Notes.
The P -value provides an alternative to the Five Steps for testing hypotheses.
(Of course both methods result in the same decision to Reject H0 or not.)
The P -value is calculated from almost the same shading as in the Rejection
Region except that we shade from the actual value of the Z statistic (Z = 1.75)
instead of from numbers (called critical values) such as Z = 1.645 or Z = 2.33
that we look up in the Z table.
When we reconsider Example 3 in the Notes,
P -value = 0.0401 = (Area to the right of Z = 1.75)
(1) As an alternative to the Five Steps used in part (a), calculate the P -value.
(2) Provide the risk interpretation of the P -value.
(3) Make a decision by comparing the P -value to the significance level.
(e) Let’s try another P -value!
,
(1) As an alternative to the Five Steps used in part (b), calculate the P -value.
(2) Provide the risk interpretation of the P -value.
(3) Make a decision by comparing the P -value to the significance level.
• Exercise 7.5 (page 401)
Ignore the book’s instructions about the P -value. Apply the Five Steps instead.
• Exercise 7.114 (page 447) Do part (a) only.
Ignore the book’s instructions about the P -value. Apply the Five Steps instead, at 5% significance.
(continued)
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• Exercise 7.23 (page 413)
Ignore textbook instructions for this exercise. Instead answer (a), (b), (c) below.
◦ There’s a MINITAB file on the Homework web page. So you can calculate x̄ and s either
on your calculator or with MINITAB Basic Statistics > Display Descriptive Statistics.
(On quizzes and exams you’ll need to use your calculator.)
(a) Suppose that Consumer’s Digest magazine is considering writing an article which claims
that the Toyota Highlander Hybrid receives fewer than 30 mpg on average when set to
60 mph on cruise control. There’s a danger that Toyota will sue Consumer’s Digest for
making a false claim so test using the Five Steps at a very cautious 1% significance level.
(b) Calculate the P -value for this test. (Refer to the end of the Topic 8 Notes if you need a
refresher.)
(c) Interpret the P -value from part (b). How does the P -value reinforce the decision from
part (a)?
• Exercise 6.117 (page 390)
Do part (c) only. (Use 5% significance.)
• Exercise 6.118 Do part (b) only.
(Reason an answer from the CI. You do not need to do the Five Steps.)
• Exercise 6.119
• Exercise 7.32 (page 415)
Ignore the textbook’s instructions.
◦ A MINITAB data file is available on the Homework page for optional use.
◦ Is there conclusive evidence that the mean IBI (water quality) differs from an environmental standard of 68 points? Use the Five Steps and 10% significance.
• Exercise 7.40
Do part (a) only.
(continued)
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• Exercise 6.122 (page 390)
Ignore textbook instructions. Instead answer (a) and (b):
◦ We’ll test the hypotheses
HA : µ > 0
H0 : µ ≤ 0
for µ = mean percentage increase in CEO salaries this year
at 5% significance using the P -value Method instead of the Five Steps.
(a) Calculate the P -value for the test.
(b) Make a decision based on the P -value. Also interpret the test.
• Exercise 6.77 (page 370)
Ignore textbook instructions. Instead answer (a) and (b):
(a) Is there significant evidence at the 5% level that the mean reading differs from the true
value 105? Use the Five Steps.
(b) Calculate and interpret the P -value for this test.
(end of assignment)
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