Practice Problems using Confidence Intervals and Hypothesis tests
1. A nylon rope maker claims its repelling rope's average breaking strength is at least 800 pounds. A
researcher sets up a hypothesis test regarding the breaking strength of the rope where Ho: μ  800. where α =
.05.
a. Rewrite his null and alternative hypotheses as complete sentences. What does the hypothesis suggest about
where the benefit of the doubt is being placed? Explain your answer.
b. What does it mean to make a type I error, and, specifically, what would constitute a type one error in this
case?
c. In this case, is it appropriate to use α = .05? Explain why or why not.
d. what would we conclude if the sample average was much larger than 800 pounds?
e. what would we conclude if the sample average was slightly less than 800 pounds?
f. what if the sample average is much less than 800?
1. Waders Inc. currently has an exclusive contract with United Airlines for all domestic air
travel. In return for the exclusive contract, United gives the company a 20 percent discount.
After the discount, an average round-trip flight on United costs the company $687 with a
standard deviation of $120. Sam Innair is the United representative that handles the Waders
Inc. Account.
Sally Flibinite represents a discount airline that is trying to get the Waders Inc. account. "Give
us a try, she says, I guarantee we'll save you money." Waders Inc agrees to a test. In a sample
of 49 flights, the discount airline's average fare was $650 with a standard deviation of $140.
Upon seeing the results, Sally proclaims the test a success.
When Waders Inc. presents United with the test results, Sam claims that you might find the
same average over a sample of their own flights, and so the results are inconclusive.
Answer the question two ways:
A. Using confidence interval for the discount airline’s population average.
B. Using a hypothesis test that gives United the benefit of the doubt.
2. Last year Alert America’s residential alarm system sales reps, sold an average of 50 systems
per salesperson. This year sales seem slower. As with most sales forces of this type, employee
turnover has been brisk, but this year the problem seems worse than usual. Last year, the
average tenure (time with the company) of an Alert America sales representative was 2.9 years
with a standard deviation of 2 years. When the company inventoried tenure in May, the average
of a random sample of thirty-six sales representatives was only 2 years, but the standard
deviation was 3 years. Management opinion is divided as to what to make of the difference.
Some think that this is just a temporary abnormality, while others think that this is evidence of
an underlying problem. As chief of statistical analysis, each side turns to you for your opinion.
Answer the question two ways:
A. Using confidence interval for the new population tenure average.
B. Using a hypothesis test that assumes nothing has changed.
3. McDonalds has been considering dropping the pickles from its burgers. There is some
sentiment that the ubiquitous pickle adds to the cost of the sandwich, but most people remove
them anyway. The CEO decides that if we can be reasonably certain more than two-thirds of
customers remove the pickle, then the pickle should no longer be placed on the sandwich
(except by request). Ronald was enlisted to spy on a random sample of one thousand
customers. He found that 69 percent removed the pickle. What should the company do and
why?
4. Mc Donalds is also considering changing pickle suppliers. With the current supplier, each
McD’s pays an average of 1 cent per pickle. A rival in a sample of 49 pickle prices from a
rival supplier (pickle prices vary by region due to shipping costs etc.) The average price was .9
cents per pickle with a standard deviation of .02 cents. Should we switch suppliers? Explain
why or why not.
5. Pennsylvania Governor Tom Ridge has a longstanding reputation for being "tough on
crime." His opponent is currently running ads that dispute this. Before Ridge took office, the
average criminal spent 10.5 years in prison before parole. Ridge's opponent says that a random
sample of forty-nine recent parolees spent an average of only ten years in prison (the standard
deviation in the sample was fourteen years). Assuming you work for an independent
newspaper, evaluate the claim made by the Ridge opponent. What would you report to your
readers?
6. Each year accounting students from colleges across the nation take the CPA exam.
Nationally, the pass rate is one-third. West Chester students traditionally fare very well on
these exams. Recently, forty-five West Chester students took the CPA exam and eighteen
passed on their first try. Can we be reasonably sure that a higher percentage West Chester
students pass the exam?