Deck 12: Comparing Two Means

Question 1

Data were collected on annual personal time (in hours) taken by a random sample of 16 women (group1) and 7 men (group 2) employed by a medium sized company. The women
Took an average of 24.75 hours of personal time per year with a standard deviation of 2.84
Hours. The men took an average of 21.89 hours of personal time per year with a standard
Deviation of 3.29 hours. The Human Resources Department believes that women tend to
Take more personal time than men because they tend to be the primary child care givers in
The family. The results of the test are t = 2.02 with an associated P-value of 0.0352. The
Correct conclusion at α = 0.05 is to

A) reject the null hypothesis.
B) fail to reject the null hypothesis.
C) conclude that women take a higher average number of hours of personal time per year
Compared to men.
D) Both A and C.
E) Both B and C.

Answer 1

Both A and C.

Question 2

Use the following for questions
An army depot that overhauls ground mobile radar systems is interested in improving its processes. One problem involves troubleshooting a particular component that has a high failure rate after it has been repaired and reinstalled in the system. The shop floor supervisor believes that having standard work procedures in place will reduce the time required for troubleshooting this component. Time (in minutes) required troubleshooting this component without and with the standard work procedure is recorded for a sample of 19 employees. Does this sample indicate that having a standard work procedure in place reduces troubleshooting time?
Write the null and alternative hypotheses.

Answer 2

Question 3

Use the following for questions
A mid-sized company has decided to implement an enterprise resource planning (ERP) system, and management suspects that many of its employees are concerned about the planned implementation. Managers are considering holding informational workshops to help decrease anxiety levels among employees. To determine whether such an approach would be effective, they randomly select 16 employees to participate in a pilot workshop.
These employees were given a questionnaire to measure anxiety levels about ERP before and after participating in the workshop. Do the data indicate that anxiety levels about ERP decreases as a result of the workshop? Determine whether two samples are independent or paired.
Create and interpret a 90% confidence interval.

Answer 3

Question 4

Are the assumptions and conditions for carrying out the t-test for two means satisfied?
Explain.

Question 5

Based on the test statistic and its P-value, state your conclusion using α = .05.

Question 6

Data were collected on annual personal time (in hours) taken by a random sample of 16 women and 7 men employed by a medium-sized company. The women took an average of 24.75 hours of personal time per year with a standard deviation of 2.84 hours. The men took an average of 21.86 hours of personal time per year with a standard deviation of 3.29 hours. The Human Resources Department believes that women tend to take more personal time than men because they tend to be the primary child care givers in the family.


Are the assumptions and conditions for carrying out the t-test for two means satisfied?
Explain.

Question 7

Create and interpret a 90% confidence interval.

Question 8

Data were collected on annual personal time (in hours) taken by a random sample of 16 women and 7 men employed by a medium sized company. The women took an average of
24)75 hours of personal time per year with a standard deviation of 2.84 hours. The men
Took an average of 21.89 hours of personal time per year with a standard deviation of 3.29
Hours. The standard error of the sampling distribution for the difference between the two
Means is

A) 2.05
B) 5.02
C) 2.24
D) 1.43
E) 0.48

Question 9

Use the following for questions
A mid-sized company has decided to implement an enterprise resource planning (ERP) system, and management suspects that many of its employees are concerned about the planned implementation. Managers are considering holding informational workshops to help decrease anxiety levels among employees. To determine whether such an approach would be effective, they randomly select 16 employees to participate in a pilot workshop.
These employees were given a questionnaire to measure anxiety levels about ERP before and after participating in the workshop. Do the data indicate that anxiety levels about ERP decreases as a result of the workshop? Determine whether two samples are independent or paired.
Write the null and alternative hypotheses.

Question 10

Data were collected on annual personal time (in hours) taken by a random sample of 16 women (group1) and 7 men (group 2) employed by a medium sized company. The women
Took an average of 24.75 hours of personal time per year with a standard deviation of 2.84
Hours. The men took an average of 21.89 hours of personal time per year with a standard
Deviation of 3.29 hours. The Human Resources Department believes that women tend to
Take more personal time than men because they tend to be the primary child care givers in
The family. The correct null and alternative hypotheses to test this belief are

A) H0: µ1 - µ2 = 0 and HA: µ1 - µ2 < 0.
B) H0: µ1 - µ2 = 0 and HA: µ1 - µ2 ≠ 0.
C) H0: µ1 - µ2 = 0 and HA: µ1 - µ2 > 0.
D) H0: µ1 - µ2 > 0 and HA: µ1 - µ2 < 0.
E) None of the above.

Question 11

Data were collected on annual personal time (in hours) taken by a random sample of 16 women and 7 men employed by a medium sized company. The women took an average of
24)75 hours of personal time per year with a standard deviation of 2.84 hours. The men
Took an average of 21.89 hours of personal time per year with a standard deviation of 3.29
Hours. The Human Resources Department believes that women tend to take more personal
Time than men because they tend to be the primary child care givers in the family. The t-
Test for two means is appropriate in this situation because

A) women and men are dependent samples.
B) women and men are independent samples.
C) women and men are matched samples.
D) the observations are paired.
E) None of the above.

Question 12

Based on the test statistic and its P-value, state your conclusion using α = .05.

Question 13

We want to know whether people are likely to offer a different amount for used
exercising equipment when buying from a friend than when buying from a stranger. We
wonder whether the difference between mean amounts is zero. We have bid prices from 8
subjects buying from a friend and 7 subjects buying from a stranger, found in a
randomized experiment.
A. What assumptions can we make?
b. What type of test can we perform?

Question 14

Use the following for questions
An army depot that overhauls ground mobile radar systems is interested in improving its processes. One problem involves troubleshooting a particular component that has a high failure rate after it has been repaired and reinstalled in the system. The shop floor supervisor believes that having standard work procedures in place will reduce the time required for troubleshooting this component. Time (in minutes) required troubleshooting this component without and with the standard work procedure is recorded for a sample of 19 employees. Does this sample indicate that having a standard work procedure in place reduces troubleshooting time?
Create and interpret a 95% confidence interval.

Question 15

Data were collected on annual personal time (in hours) taken by a random sample of 16 women and 7 men employed by a medium-sized company. The women took an average of 24.75 hours of personal time per year with a standard deviation of 2.84 hours. The men took an average of 21.86 hours of personal time per year with a standard deviation of 3.29 hours. The Human Resources Department believes that women tend to take more personal time than men because they tend to be the primary child care givers in the family.


Write the null and alternative hypotheses.

Question 16

Write the null and alternative hypotheses.

Question 17

Use the following for questions
A mid-sized company has decided to implement an enterprise resource planning (ERP) system, and management suspects that many of its employees are concerned about the planned implementation. Managers are considering holding informational workshops to help decrease anxiety levels among employees. To determine whether such an approach would be effective, they randomly select 16 employees to participate in a pilot workshop.
These employees were given a questionnaire to measure anxiety levels about ERP before and after participating in the workshop. Do the data indicate that anxiety levels about ERP decreases as a result of the workshop? Determine whether two samples are independent or paired.
Based on the test statistic and its P-value, state your conclusion using α = .05.

Question 18

Create and interpret a 90% confidence interval.

Question 19

Use the following for questions
An army depot that overhauls ground mobile radar systems is interested in improving its processes. One problem involves troubleshooting a particular component that has a high failure rate after it has been repaired and reinstalled in the system. The shop floor supervisor believes that having standard work procedures in place will reduce the time required for troubleshooting this component. Time (in minutes) required troubleshooting this component without and with the standard work procedure is recorded for a sample of 19 employees. Does this sample indicate that having a standard work procedure in place reduces troubleshooting time?
Are the assumptions and conditions for carrying out the paired t-test satisfied?
Explain.

Question 20

Use the following for questions
A mid-sized company has decided to implement an enterprise resource planning (ERP) system, and management suspects that many of its employees are concerned about the planned implementation. Managers are considering holding informational workshops to help decrease anxiety levels among employees. To determine whether such an approach would be effective, they randomly select 16 employees to participate in a pilot workshop.
These employees were given a questionnaire to measure anxiety levels about ERP before and after participating in the workshop. Do the data indicate that anxiety levels about ERP decreases as a result of the workshop? Determine whether two samples are independent or paired.
Are the assumptions and conditions for carrying out the paired t-test satisfied?
Explain.

Question 21

An army depot that overhauls ground mobile radar systems is interested in improving its processes. One problem involves troubleshooting a particular component that has a high
Failure rate after it has been repaired and reinstalled in the system. The shop floor
Supervisor believes that having standard work procedures in place will reduce the time
Required for troubleshooting this component. Time (in minutes) required troubleshooting
This component without and with the standard work procedure is recorded for a sample of
19 employees. The P-value associated with the calculated test statistic is < 0.001. At α =
0)05, the correct conclusion is to

A) reject the null hypothesis.
B) fail to reject the null hypothesis.
C) conclude that having standard work procedures in place reduces troubleshooting time for
This component.
D) Both A and C.
E) Both B and C.

Question 22

A mid-sized company has decided to implement an enterprise resource planning (ERP) system, and management suspects that many of its employees are concerned about the
Planned implementation. Managers are considering holding informational workshops to
Help decrease anxiety levels among employees. They randomly select 16 employees to
Participate in a pilot workshop. These employees were given a questionnaire to measure
Anxiety levels about ERP before and after participating in the workshop. At the 90%
Confidence level, what is the margin of error for the mean difference in anxiety levels pre- and post-workshop?

A) 1.753
B) 1.147
C) 0.287
D) 0.503
E) 2.010

Question 23

Question 24

Data were collected on annual personal time (in hours) taken by a random sample of 16 women and 20 men employed by a medium-sized company. The women took an average
Of 24.75 hours of personal time per year with a standard deviation of 2.84 hours. The men
Took an average of 20.5 hours of personal time per year with a standard deviation of 2.75
Hours. The pooled estimate of the variance is

A) 264.6715
B) 2.790
C) 7.785
D) 12.998
E) None of the above.

Question 25

A mid-sized company has decided to implement an enterprise resource planning (ERP) system, and management suspects that many of its employees are concerned about the Planned implementation. Managers are considering holding informational workshops to Help decrease anxiety levels among employees. They randomly select 16 employees to Participate in a pilot workshop. These employees were given a questionnaire to measure Anxiety levels about ERP before and after participating in the workshop. If we let d = post-workshop anxiety level - pre-workshop anxiety level, the correct alternative hypothesis to determine if this approach was successful is

A)
B)
C)
D)
E)

Question 26

An army depot that overhauls ground mobile radar systems is interested in improving its processes. One problem involves troubleshooting a particular component that has a high
Failure rate after it has been repaired and reinstalled in the system. The shop floor
Supervisor believes that having standard work procedures in place will reduce the time
Required for troubleshooting this component. Time (in minutes) required troubleshooting
This component without and with the standard work procedure is recorded for a sample of
19 employees. Assuming that we define our differences as Time without standard work
Procedure - Time with standard work procedure, the correct alternative hypothesis is

A) µd = 0.
B) µd < 0.
C) µd > 0.
D) µd ≠ 0.
E) None of the above.

Question 27

A consumer group was interested in comparing the operating time of cordless toothbrushes manufactured by two different companies. Group members took a random Sample of 18 toothbrushes from Company A and 15 from Company B. Each was charged Overnight and the number of hours of use before needing to be recharged was recorded. Company A toothbrushes operated for an average of 119.7 hours with a standard deviation Of 1.74 hours; Company B toothbrushes operated for an average of 120.6 hours with a Standard deviation of 1.72 hours. The 90% confidence interval is (-1.93, 0.13). The correct Interpretation is

A) We are 90% confident that, on average, there is no difference in operating hours Between toothbrushes from Company A compared to those from Company B.
B) We are 90% confident that, on average, the toothbrushes from Company A operate Longer before needing to be recharged than the toothbrushes from Company B.
C) We are 90% confident that, on average, the toothbrushes from Company B operate Longer before needing to be recharged than the toothbrushes from Company A.
D) We are 90% confident that, on average, there is a difference in operating hours between Toothbrushes from Company A compared to those from Company B.
E) None of the above.

Question 28

Data were collected on annual personal time (in hours) taken by a random sample of 16 women and 7 men employed by a medium sized company. The women took an average of 24.75 hours of personal time per year with a standard deviation of 2.84 hours. The men took an average of 21.89 hours of personal time per year with a standard deviation of 3.29 hours. The correct 90% confidence interval for the difference between women and men in the average number of hours of personal time taken per year is

A) 0.30 to 5.48 hours.
B) -0.50 to 3.21 hours.
C) -4.67 to -0.62 hours.
D) 1.27 to 6.89 hours.
E) None of the above.

Question 29

A consumer group was interested in comparing the operating time of cordless toothbrushes manufactured by two different companies. Group members took a random
Sample of 18 toothbrushes from Company A and 15 from Company B. Each was charged
Overnight and the number of hours of use before needing to be recharged was recorded.
Company A toothbrushes operated for an average of 119.7 hours with a standard deviation of 1.74 hours; Company B toothbrushes operated for an average of 120.6 hours with a standard deviation of 1.72 hours. The t-test for two means is appropriate in this situation because

A) the two companies are dependent.
B) the two companies are independent.
C) the two companies are matched samples.
D) the observations are paired.
E) None of the above.

Question 30

Data were collected on annual personal time (in hours) taken by a random sample of 16 women and 20 men employed by a medium-sized company. The women took an average
Of 24.75 hours of personal time per year with a standard deviation of 2.84 hours. The men took an average of 20.5 hours of personal time per year with a standard deviation of 2.75 hours. If we use the pooled t-test to see if there is a difference between the two groups,the degrees of freedom for the appropriate t-statistic is

A) 36
B) 34
C) 20
D) 16
E) None of the above.

Question 31

A consumer group was interested in comparing the operating time of cordless toothbrushes manufactured by two different companies. Group members took a random
Sample of 18 toothbrushes from Company A and 15 from Company B. Each was charged
Overnight and the number of hours of use before needing to be recharged was recorded.
Company A toothbrushes operated for an average of 119.7 hours with a standard deviation of 1.74 hours; Company B toothbrushes operated for an average of 120.6 hours with a standard deviation of 1.72 hours. Do these samples indicate that Company B toothbrushes operate more hours on average than Company A toothbrushes? The correct hypotheses to address this question are

A) H0: µA - µB = 0 and HA: µA - µB < 0
B) H0: µA - µB = 0 and HA: µA - µB ≠ 0.
C) H0: µA - µB = 0 and HA: µA - µB > 0.
D) H0: µA - µB > 0 and HA: µA - µB < 0.
E) None of the above.

Question 32

A mid-sized company has decided to implement an enterprise resource planning (ERP) system, and management suspects that many of its employees are concerned about the
Planned implementation. Managers are considering holding informational workshops to
Help decrease anxiety levels among employees. To determine whether such an approach
Would be effective, they randomly select 16 employees to participate in a pilot workshop.
These employees were given a questionnaire to measure anxiety levels about ERP before
And after participating in the workshop. To determine if anxiety levels about ERP
Decreases as a result of the workshop, they should use a

A) one-tailed paired t-test.
B) two-tailed test of two independent means.
C) one-tailed test of two independent means.
D) two-tailed paired t-test.
E) one-tailed test of two proportions.

Question 33

Results of a small experiment show that people are likely to offer a different amount for used exercise equipment when bargaining with a friend than when bargaining with a
Stranger. The p-value from testing the difference in mean offers was equal to 0.00162.
At an α = 0.05, the correct conclusion is to

A) reject the null hypothesis.
B) fail to reject the null hypothesis.
C) conclude that there is no difference between bargaining with a stranger versus a friend.
D) Both A and C.
E) Both B and C.

Question 34

Managers are considering holding informational workshops to help decrease anxiety levels among employees. They randomly select 20 employees to participate in a pilot
Workshop. These employees were given a questionnaire to measure anxiety levels before
And after participating in the workshop. A test was performed to determine if the workshop
Was successful in decreasing anxiety levels. The test results yielded a P-value of 0.008.
The correct conclusion at α = .05 is

A) to accept the null hypothesis.
B) to reject the null hypothesis.
C) to conclude that participating in the workshop decreases employee anxiety about ERP.
D) both A and C.
E) both B and C.

Question 35

An army depot that overhauls ground mobile radar systems is interested in improving its processes. One problem involves troubleshooting a particular component that has a high
Failure rate after it has been repaired and reinstalled in the system. The shop floor
Supervisor believes that having standard work procedures in place will reduce the time
Required for troubleshooting this component. Time (in minutes) required troubleshooting
This component without and with the standard work procedure is recorded for a sample of
19 employees. In order to determine if having a standard work procedure in place reduces
Troubleshooting time, they should use

A) a one-tailed paired t-test.
B) a two-tailed test of two independent means.
C) a one-tailed test of two independent means.
D) a two-tailed paired t-test.
E) a test of two proportions.

Question 36

Which of the following is not an assumption and/or condition for the paired t-test?

A) Nearly Normal Condition
B) Independent Groups Assumption
C) Paired Data Assumption
D) Randomization Condition
E) All of the above