Exercises- Chapter 9 Hypothesis Testing: One-Sample Tests
Exercises adopted from the textbook Basic Business Statistics 15th Edition by Mark Berenson, David Levine,
Kathryn Szabat and David Stephan. They are helpful for your Homework.
Section 9.2: Hypothesis Test Approaches and
Z Test of Hypothesis for the Mean with σ Known (Two-Tailed)
Exercise 9.2. If you use a 0.05 level of significance in a two-tail hypothesis test, what decision will you
make if ZSTAT=+2.21?
(a) Determine the decision rule
(b) State your conclusion:
Exercise 9.6. What is the p-value if, in a two-tail hypothesis test, ZSTAT =+2.00
Exercise 9.7. In Exercise 9.6, what is your statistical decision if you test the null hypothesis at the 0.05
level of significance?
Exercise 9.14. The quality-control manager at a light emitting diode (LED) factory needs to determine
whether the mean life of a large shipment of LEDs is equal to 50,000 hours.
The population standard deviation is 1,500 hours. A random sample of 64 LEDs indicates a sample mean
life of 49,875 hours.
a. At the 0.05 level of significance, is there evidence that the mean life is different from 50,000 hours?
b. Compute the p-value and interpret its meaning.
c. Construct a 95% confidence interval estimate of the population mean life of the LEDs.
d. Compare the results of (a) and (c). What conclusions do you reach?
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Section 9.3: t-Test of Hypothesis for the Mean with σ Unknown (Two-Tailed)
Exercise 9.18 If, in a sample of n = 20 selected from a normal population, 𝑋 = 56 and S = 12, what is the
value of tSTAT if you are testing the null hypothesis H0: μ = 50?
Exercise 9.19 In Exercise 9.18, how many degrees of freedom does the t test have?
Exercise 9.20 In Exercises 9.18 and 9.19, what are the critical values of t if the level of significance, α, is
0.05 and the alternative hypothesis, H1: µ ≠ 50?
Exercise 9.27 The U.S. Department of Transportation requires tire manufacturers to provide performance
information on tire sidewalls to help prospective buyers make their purchasing decisions. One very
important piece of information is the tread wear index, which indicates the tire’s resistance to tread
wear. A tire with a grade of 200 should last twice as long, on average, as a tire with a grade of 100.
A consumer organization wants to test the actual tread wear index of a brand name of tires that claims
“graded 200” on the sidewall of the tire. A random sample of n =28 indicates a sample mean tread wear
index of 198.8 and a sample standard deviation of 21.4.
a. Is there evidence that the population mean tread wear index is different from 200? (Use a 0.05 level
of significance.)
b. Determine the p-value and interpret its meaning.
Section 9.3: One-Tail Tests
Exercise 9.36 In a one-tail hypothesis test where you reject H0 only in the upper tail, what is the p-value
if ZSTAT=+2.00?
Exercise 9.37 In Exercise 9.36, what is your statistical decision if you test the null hypothesis at the 0.05
level of significance?
Exercise 9.38(H) In a one-tail hypothesis test where you reject H0 only in the lower tail, what is the pvalue if ZSTAT=−1.38?
Exercise 9.39(H) In Exercise 9.38, what is your statistical decision if you test the null hypothesis at the
0.01 level of significance?
Exercise 9.47 CarMD reports that the mean repair cost of a Lexus LX350 in 2022 for a “check engine”
light was $95.
Suppose a sample of 100 “check engine” light repairs completed in the last month was selected. The
sample mean repair cost was $117 with the sample standard deviation of $25.
a. Is there evidence that the population mean repair cost is more than $95? (Use a 0.05 level of
significance.)
b. Determine the p-value and interpret its meaning.
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Exercise 9.4.47-T(H) A report states that the cost of repairing a hybrid vehicle is falling even while typical
repairs on conventional vehicles are getting more expensive. The most common hybrid repair, replacing
the hybrid inverter assembly, had a mean repair cost of $3,927 in 2012. Industry experts suspect that the
cost will continue to decrease given the increase in the number of technicians who have gained expertise
on fixing gas-electric engines in recent months. Suppose a sample of 100
hybrid inverter assembly repairs completed in the last month was selected. The sample mean repair cost
was $3,880 with the sample standard deviation of $400. Complete parts (a) and (b) below.
a. Is there evidence that the population mean cost is less than $3,927? (Use a 0.10 level of significance.)
b. Determine the p-value and interpret its meaning.
Section 9.5: Z-Test of Hypothesis for the Proportion
Exercise 9.59. A cellphone provider has the business objective of wanting to determine the proportion of
subscribers who would upgrade to a new cellphone with improved features if it were made available at a
substantially reduced cost. Data are collected from a random sample of 500 subscribers. The results
indicate that 155 of the subscribers would upgrade to a new cellphone at a reduced cost.
a. At the 0.05 level of significance, is there evidence that more than 20% of the subscribers would
upgrade to a new cellphone at a reduced cost?
b. How would the manager in charge of promotional programs concerning subscribers use the results
in (a)?
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Exercises Outside the Textbook
Problem 9.1: Suppose a processing plant will close down a production line for maintenance if
the average length of time a robot welder takes to complete the weld is not 1.919 minutes.
You want to test whether the production line should be closed for maintenance.
a. What is the appropriate null hypothesis?
b. What is the appropriate alternative hypothesis?
Problem 9.2: Consider the following hypothesis test:
Ho: µ < 22
Ha:µ > 22
A sample of 75 is used and the population standard deviation σ is 10. Use the critical value
approach to state your conclusion for each of the sample result. Use α = 0.05.
a. x = 23
b. x = 25
Hypothesis Test:
Step 1: State Ho, H1
Step 2: Specify level of significant and sample size
Use z-Test for
Mean when σ
is known
Step 3: Determine the appropriate test technique
Step 4: Find the critical value and rejection rule
The critical value =
Rejection rule:
𝑥̄ −𝜇0
Step 5: Compute Test statistic ZSTAT = 𝜎
⁄ 𝑛
√
Step 6: Make Statistical Decision:


Determine whether to reject Ho
Write your conclusion in complete sentences in response to hypothesis test
question.
Problem 9.3: Find the following p-values associated with each of the scenarios below.
a. If the hypothesis is HA: μ < 14 oz and the associated test statistic is z = – 1.63
b. If the hypothesis is HA: μ > 3” and the associated test statistic is z = 2.01
c. If the hypothesis is HA: μ ≠ $27 and the associated test statistic is z = – 2.01
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Problem 9.4: A manufacturing company produces valves of different sizes and shapes. One
valve plate is supposed to have a tensile strength of 5 lbs/mm and is known to have a standard
deviation of 0.28 lbs/mm. The company tests a randomly selected sample of 32 valve plates and
finds the plates have an average tensile strength of 4.9289 lbs/mm.
a.. State the appropriate values from the problem.
Hypothesized Population Mean, μ0 =
; Population standard deviation,  
Sample size, n 
; Sample mean, x 
b. Conduct a hypothesis test using the z-statistic to determine whether there is sufficient
evidence to conclude with level of significant α = 0.05 that the average tensile strength of the
sample differs from the company’s standard. Use p-value approach.
Hypothesis Test:
Step 1: State Ho, Ha
H0 :
H1:
Step 2: Specify level of significant and sample size
Step 3: Determine the appropriate test technique
𝑥̄ −𝜇0
Step 4: Compute Test statistic ZSTAT = 𝜎
⁄ 𝑛
√
The p-value =
Rejection rule:
Step 5: Make Statistical Decision:


Determine whether to reject Ho
Write your conclusion in complete sentences in response to hypothesis test question.
Problem 9.5: In order to determine the average price of hotel rooms in Atlanta, a sample
of 64 hotels was selected. It was determined that the average price of the rooms in the
sample was $108.50 with a sample standard deviation s of $16.
a. Formulate the hypotheses to determine whether or not the average room price
is significantly different from $112.
b. Compute the test statistic.
c. At 95% confidence (equivalently α = 0.05), the p-value = 0.0849.
Should H0 be rejected? What is your conclusion from this hypothesis testing for the
mean price of hotel rooms in Atlanta?
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Problem 9.6 : Easy-Fly Airline took a random sample of 25 flights to determine if the mean time
it takes for luggage to reach the travelers departing from a flight is less than 15 minutes. The
sample mean was found to be 13.8 minutes with a sample standard deviation s of 4 minutes.
Using a significance level of 0.05 and critical-value approach, what conclusion can be reached
based on the random sample?
Hypothesis Test:
Step 1: State Ho, Ha
H0 :
H1 :
Step 2: Specify level of significant and sample size
Step 3: Determine the appropriate test technique
Use t-Test for
Mean when σ is
unknown
Step 4: Find the critical value and rejection rule
The critical value =
Rejection rule:
𝑥̄ −𝜇0
Step 5: Compute Test statistic tSTAT = 𝑠
⁄ 𝑛
√
Step 6: Make Statistical Decision:


Determine whether to reject Ho
Write your conclusion in complete sentences in response to hypothesis test question.
Problem 9.7: StatCounter estimates that 35% of worldwide Internet users utilized Chrome as
their primary browser. Last term, 100 Fresno State students were asked about their browser
preferences, approx. 41% of students surveyed preferred Chrome. Conduct an appropriate test
and use the critical-value approach to determine if the proportion of Fresno State students who
use Chrome is significant greater than Internet users in general. Assume the level of significant
of 10%.
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Problem 9.8: Harper’s Index claims that 23% of American are in favour of outlawing cigarettes.
You decide to test this claim and ask a random sample of 200 Americans whether they are in
favour of outlawing cigarettes. Out of 200 Americans, 54 are in favour. Use critical-value or pvalue approach and a significance level of 0.05. Conduct a hypothesis test to determine whether
there is enough evidence to reject the claim.
a. What type of test to use? (Circle one)
Z-Test for mean
proportion
t-Test for mean
Z-Test for population
b. Conduct a hypothesis test. Is there enough evidence to reject the claim?
Step 1: State Ho, H1
H0 :
H1 :
Step 2: Specify level of significant and sample size
Step 3: Determine the appropriate test technique
Step 4: Find the critical value and rejection rule
The critical value =
Rejection rule:
Step 5: Compute Test statistic ZSTAT
The p-value =
Rejection rule:
Step 6: Make Statistical Decision:


Determine whether to reject Ho
Write your conclusion in complete sentences in response to hypothesis test question.
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Problem 9.9 (Criminal Trial): Generally, the basic principles are that the court assumes
fundamentally the suspect is innocent, but the prosecutor must prove the guilt of defendant. The
criminal trial in fact could be viewed from Hypothesis Test with
Ho: The defendant is innocent
HA: The defendant committed the crime
The conclusion is either (1) the defendant did not commit the crime (Accept Ho or Fail to Reject
Ho) and let him/her go free, or (2) the defendant committed the crime (Reject Ho) and he/she
goes to jail.
1. Which of the following is the type I error? Which is Type II error?
a. Convicting an innocent person that is an innocent person goes to jail.
b. Letting a guilty person goes free.
Problem 9.10: In the pregnancy test, the possible state of nature 1) the person is pregnant; 2) the
person is not pregnant.
a. What is the appropriate null hypothesis?
b. What is the appropriate alternative hypothesis?
HINT: HA contains the original state of nature (no change). The reason to conduct the
hypothesis test is contained in HA.
c. Which of the following is the type I error? Which is Type II error?
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