Question 1

SCENARIO 9-1
Microsoft Excel was used on a set of data involving the number of defective items found in a random
sample of 46 cases of light bulbs produced during a morning shift at a plant. A manager wants to
know if the mean number of defective bulbs per case is greater than 20 during the morning shift. She
will make her decision using a test with a level of significance of 0.10. The following information
was extracted from the Microsoft Excel output for the sample of 46 cases: $n = 46$; Arithmetic Mean $= 28.00$; Standard Deviation $= 25.92$; Standard Error $= 3.82$;
Null Hypothesis: $H _ { 0 } : \mu \leq 20 ; \alpha = 0.10 ; \mathrm { df } = 45 ; T$ Test Statistic $= 2.09$;
One-Tail Test Upper Critical Value $= 1.3006 ; p$-value $= 0.021 ;$ Decision $=$ Reject.
-In conducting research, you should document both good and bad results.

Accepted Answer

A) True 
 B)False

Question 2

SCENARIO 9-9
The president of a university claimed that the entering class this year appeared to be larger than the
entering class from previous years but their mean SAT score is lower than previous years. He took a
sample of 20 of this year's entering students and found that their mean SAT score is 1,501 with a
standard deviation of 53. The university's record indicates that the mean SAT score for entering
students from previous years is 1,520. He wants to find out if his claim is supported by the evidence
at a 5% level of significance.
-Referring to Scenario 9-9, state the alternative hypothesis for this study.

Accepted Answer

The answer of SCENARIO 9-9
The president of a university claimed...

Question 3

SCENARIO 9-3
An appliance manufacturer claims to have developed a compact microwave oven that consumes a
mean of no more than 250 W. From previous studies, it is believed that power consumption for
microwave ovens is normally distributed with a population standard deviation of 15 W. A consumer
group has decided to try to discover if the claim appears true. They take a sample of 20 microwave
ovens and find that they consume a mean of 257.3 W.
-Referring to Scenario 9-3, the appropriate hypotheses to determine if the manufacturer's claim appears reasonable are: a) $H _ { 0 } : \mu = 250$ versus $H _ { 1 } : \mu \neq 250$
b) $H _ { 0 } : \mu \geq 250$ versus $H _ { 1 } : \mu < 250$
c) $H _ { 0 } : \mu \leq 250$ versus $H _ { 1 } : \mu > 250$
d) $H _ { 0 } : \mu \geq 257.3$ versus $H _ { 1 } : \mu < 257.3$

Accepted Answer

The answer of SCENARIO 9-3
An appliance manufacturer claims to have...

Question 4

SCENARIO 9-8
One of the biggest issues facing e-retailers is the ability to turn browsers into buyers. This is
measured by the conversion rate, the percentage of browsers who buy something in their visit to a
site. The conversion rate for a company's website was 10.1%. The website at the company was
redesigned in an attempt to increase its conversion rates. A sample of 200 browsers at the redesigned
site was selected. Suppose that 24 browsers made a purchase. The company officials would like to
know if there is evidence of an increase in conversion rate at the 5% level of significance.
-Referring to Scenario 9-8, state the null hypothesis for this study.

Accepted Answer

The answer of SCENARIO 9-8
One of the biggest issues facing...

Question 5

SCENARIO 9-1
Microsoft Excel was used on a set of data involving the number of defective items found in a random
sample of 46 cases of light bulbs produced during a morning shift at a plant. A manager wants to
know if the mean number of defective bulbs per case is greater than 20 during the morning shift. She
will make her decision using a test with a level of significance of 0.10. The following information
was extracted from the Microsoft Excel output for the sample of 46 cases: $n = 46$; Arithmetic Mean $= 28.00$; Standard Deviation $= 25.92$; Standard Error $= 3.82$;
Null Hypothesis: $H _ { 0 } : \mu \leq 20 ; \alpha = 0.10 ; \mathrm { df } = 45 ; T$ Test Statistic $= 2.09$;
One-Tail Test Upper Critical Value $= 1.3006 ; p$-value $= 0.021 ;$ Decision $=$ Reject.
-Referring to Scenario 9-1, if these data were used to perform a two-tail test, the p-
value would be 0.042.

Accepted Answer

A) True 
 B)False

Question 6

SCENARIO 9-1
Microsoft Excel was used on a set of data involving the number of defective items found in a random
sample of 46 cases of light bulbs produced during a morning shift at a plant. A manager wants to
know if the mean number of defective bulbs per case is greater than 20 during the morning shift. She
will make her decision using a test with a level of significance of 0.10. The following information
was extracted from the Microsoft Excel output for the sample of 46 cases: $n = 46$; Arithmetic Mean $= 28.00$; Standard Deviation $= 25.92$; Standard Error $= 3.82$;
Null Hypothesis: $H _ { 0 } : \mu \leq 20 ; \alpha = 0.10 ; \mathrm { df } = 45 ; T$ Test Statistic $= 2.09$;
One-Tail Test Upper Critical Value $= 1.3006 ; p$-value $= 0.021 ;$ Decision $=$ Reject.
-Referring to Scenario 9-1, the null hypothesis would be rejected if a 5% probability
of committing a Type I error is allowed.

Accepted Answer

A) True 
 B)False

Question 7

SCENARIO 9-3
An appliance manufacturer claims to have developed a compact microwave oven that consumes a
mean of no more than 250 W. From previous studies, it is believed that power consumption for
microwave ovens is normally distributed with a population standard deviation of 15 W. A consumer
group has decided to try to discover if the claim appears true. They take a sample of 20 microwave
ovens and find that they consume a mean of 257.3 W.
-Referring to Scenario 9-3, the p-value of the test is ________.

Accepted Answer

The answer of SCENARIO 9-3
An appliance manufacturer claims to have...

Question 8

The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is Greater than 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no Entertainment changes will be made. If she wants to have a level of significance at 0.01, what Rejection region should she use? a) Reject $H _ { 0 }$ if $t < - 2.3263$. b) Reject $H _ { 0 }$ if $t < - 2.5758$. c) Reject $H _ { 0 }$ if $t > 2.3263$. d) Reject $H _ { 0 }$ if $t > 2.5758$.

Accepted Answer

The answer of The owner of a local nightclub has...

Question 9

The power of a test is measured by its capability of

Accepted Answer

A)  rejecting a null hypothesis that is true. 
B)  not rejecting a null hypothesis that is true. 
C)  rejecting a null hypothesis that is false. 
D)  not rejecting a null hypothesis that is false.

Question 10

SCENARIO 9-10
A manufacturer produces light bulbs that have a mean life of at least 500 hours when the production
process is working properly. Based on past experience, the population standard deviation is 50 hours
and the light bulb life is normally distributed. The operations manager stops the production process if
there is evidence that the population mean light bulb life is below 500 hours.
-Referring to Scenario 9-10, if you select a sample of 100 light bulbs and are willing to have a
level of significance of 0.05, the probability of the operations manager incorrectly stopping the
process when the process is in fact working properly is _____.

Accepted Answer

The answer of SCENARIO 9-10
A manufacturer produces light bulbs that...

Question 11

SCENARIO 9-1
Microsoft Excel was used on a set of data involving the number of defective items found in a random
sample of 46 cases of light bulbs produced during a morning shift at a plant. A manager wants to
know if the mean number of defective bulbs per case is greater than 20 during the morning shift. She
will make her decision using a test with a level of significance of 0.10. The following information
was extracted from the Microsoft Excel output for the sample of 46 cases: $n = 46$; Arithmetic Mean $= 28.00$; Standard Deviation $= 25.92$; Standard Error $= 3.82$;
Null Hypothesis: $H _ { 0 } : \mu \leq 20 ; \alpha = 0.10 ; \mathrm { df } = 45 ; T$ Test Statistic $= 2.09$;
One-Tail Test Upper Critical Value $= 1.3006 ; p$-value $= 0.021 ;$ Decision $=$ Reject.
-Referring to Scenario 9-1, the parameter the manager is interested in is:

Accepted Answer

A)  the mean number of defective light bulbs per case produced at the plant. 
B)  the mean number of defective light bulbs per case among the 46 cases. 
C)  the mean number of defective light bulbs per case produced during the morning shift. 
D)  the proportion of cases with defective light bulbs produced at the plant.

Question 12

SCENARIO 9-10
A manufacturer produces light bulbs that have a mean life of at least 500 hours when the production
process is working properly. Based on past experience, the population standard deviation is 50 hours
and the light bulb life is normally distributed. The operations manager stops the production process if
there is evidence that the population mean light bulb life is below 500 hours.
-Referring to Scenario 9-10, if you select a sample of 100 light bulbs and are willing to have a
level of significance of 0.05, the probability of the operations manager not stopping the process
when the process is in fact working properly is in fact below 500 hours is _____.

Accepted Answer

The answer of SCENARIO 9-10
A manufacturer produces light bulbs that...

Question 13

SCENARIO 9-2
A student claims that he can correctly identify whether a person is a business major or an agriculture
major by the way the person dresses. Suppose in actuality that if someone is a business major, he can
correctly identify that person as a business major 87% of the time. When a person is an agriculture
major, the student will incorrectly identify that person as a business major 16% of the time. Presented
with one person and asked to identify the major of this person (who is either a business or an
agriculture major), he considers this to be a hypothesis test with the null hypothesis being that the
person is a business major and the alternative that the person is an agriculture major.
-Referring to Scenario 9-2, what is the power of the test?

Accepted Answer

A)  0.13 
B)  0.16 
C)  0.84 
D)  0.87

Question 14

SCENARIO 9-8
One of the biggest issues facing e-retailers is the ability to turn browsers into buyers. This is
measured by the conversion rate, the percentage of browsers who buy something in their visit to a
site. The conversion rate for a company's website was 10.1%. The website at the company was
redesigned in an attempt to increase its conversion rates. A sample of 200 browsers at the redesigned
site was selected. Suppose that 24 browsers made a purchase. The company officials would like to
know if there is evidence of an increase in conversion rate at the 5% level of significance.
-Referring to Scenario 9-8, what will be the p-value if these data were used to perform a two-tail
test?

Accepted Answer

The answer of SCENARIO 9-8
One of the biggest issues facing...

Question 15

SCENARIO 9-11-B
You are the quality control manager of a water bottles company. One of the biggest complaints in the
past years has been the breakage and, hence, the concern on the durability of the connector between
the lid and the bottle which many users use as a handle for the bottles. To collect evidence before
implementing any modification to the production process, your department has subjected 50 water
bottle to durability test and the following data on the number of times the handles have been used to
lift the bottles before they break are contained in the file Scenario9-11-DataB.XLSX. $$\begin{array} { l l l l l l l l l l } 
1493 & 1506 & 1515 & 1491 & 1500 & 1505 & 1517 & 1510 & 1506 & 1503 \
1503 & 1491 & 1495 & 1496 & 1496 & 1505 & 1493 & 1486 & 1504 & 1483 \
1514 & 1494 & 1497 & 1501 & 1493 & 1490 & 1510 & 1494 & 1494 & 1495 \
1494 & 1486 & 1495 & 1506 & 1506 & 1507 & 1502 & 1498 & 1510 & 1501 \
1500 & 1505 & 1492 & 1486 & 1501 & 1496 & 1501 & 1521 & 1510 & 1498
\end{array}$$ Assume that the number of times the handles have been used to lift the bottles before they break
follows a normal distribution. You want to test to see if there is enough evidence that the mean
number of times the handles have been used to lift the bottles before they break is more than 1500.
-Referring to Scenario 9-11-B, the p-value of the test is ________.

Accepted Answer

The answer of SCENARIO 9-11-B
You are the quality control manager...

Question 16

SCENARIO 9-7
A major home improvement store conducted its biggest brand recognition campaign in the company's
history. A series of new television advertisements featuring well-known entertainers and sports
figures were launched. A key metric for the success of television advertisements is the proportion of
viewers who "like the ads a lot". A study of 1,189 adults who viewed the ads reported that 230
indicated that they "like the ads a lot." The percentage of a typical television advertisement receiving
the "like the ads a lot" score is believed to be 22%. Company officials wanted to know if there is
evidence that the series of television advertisements are less successful than the typical ad (i.e. if there
is evidence that the population proportion of "like the ads a lot" for the company's ads is less than
0.22) at a 0.01 level of significance.
-Referring to Scenario 9-7, what critical value should the company officials use to determine the
rejection region?

Accepted Answer

The answer of SCENARIO 9-7
A major home improvement store conducted...

Question 17

For a given sample size n, if the level of significance ( $\alpha$ ) is decreased, the power of the test

Accepted Answer

A)  will increase. 
B)  will decrease. 
C)  will remain the same. 
D)  cannot be determined.

Question 18

SCENARIO 9-8
One of the biggest issues facing e-retailers is the ability to turn browsers into buyers. This is
measured by the conversion rate, the percentage of browsers who buy something in their visit to a
site. The conversion rate for a company's website was 10.1%. The website at the company was
redesigned in an attempt to increase its conversion rates. A sample of 200 browsers at the redesigned
site was selected. Suppose that 24 browsers made a purchase. The company officials would like to
know if there is evidence of an increase in conversion rate at the 5% level of significance.
-Referring to Scenario 9-8, state the alternative hypothesis for this study.

Accepted Answer

The answer of SCENARIO 9-8
One of the biggest issues facing...

Question 19

SCENARIO 9-2
A student claims that he can correctly identify whether a person is a business major or an agriculture
major by the way the person dresses. Suppose in actuality that if someone is a business major, he can
correctly identify that person as a business major 87% of the time. When a person is an agriculture
major, the student will incorrectly identify that person as a business major 16% of the time. Presented
with one person and asked to identify the major of this person (who is either a business or an
agriculture major), he considers this to be a hypothesis test with the null hypothesis being that the
person is a business major and the alternative that the person is an agriculture major.
-Referring to Scenario 9-2, what would be a Type II error?

Accepted Answer

A)  Saying that the person is a business major when in fact the person is a business major. 
B)  Saying that the person is a business major when in fact the person is an agriculture major. 
C)  Saying that the person is an agriculture major when in fact the person is a business major. 
D)  Saying that the person is an agriculture major when in fact the person is an agriculture major.

Question 20

SCENARIO 9-2
A student claims that he can correctly identify whether a person is a business major or an agriculture
major by the way the person dresses. Suppose in actuality that if someone is a business major, he can
correctly identify that person as a business major 87% of the time. When a person is an agriculture
major, the student will incorrectly identify that person as a business major 16% of the time. Presented
with one person and asked to identify the major of this person (who is either a business or an
agriculture major), he considers this to be a hypothesis test with the null hypothesis being that the
person is a business major and the alternative that the person is an agriculture major.
-Referring to Scenario 9-2, what is the value of $\beta$ ?

Accepted Answer

A)  0.13 
B)  0.16 
C)  0.84 
D)  0.87

Exam 9: Fundamentals of Hypothesis Testing: One-Sample Tests

The power of a test is measured by its capability of

For a given sample size n, if the level of significance ( α\alphaα ) is decreased, the power of the test

For a given sample size n, if the level of significance ( $\alpha$ ) is decreased, the power of the test