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 correct null and alternative hypotheses to test this belief are A) $ \mathrm{H}_{0:} \mu_{1}-\mu_{2}=0 $ and $ \mathrm{H}_{\mathrm{A}:} \mu_{1}-\mu_{2}<0 $. B) $ \mathrm{H}_{0:} \mu_{1}-\mu_{2}=0 $ and $ \mathrm{H}_{\mathrm{A}:} \mu_{1}-\mu_{2} \neq 0 $. C) $ \mathrm{H}_{0:} \mu_{1}-\mu_{2}=0 $ and $ \mathrm{H}_{\mathrm{A}:} \mu_{1}-\mu_{2}>0 $. D) $ \mathrm{H}_{0:} \mu_{1}-\mu_{2}>0 $ and $ \mathrm{H}_{\mathrm{A}:} \mu_{1}-\mu_{2}<0 $. E) None of the above.

Accepted Answer

The null hypothesis should always assume no difference between the two groups, so H0: μ1 -μ2 = 0 is correct. Since the Human Resources Department believes that women tend to take more personal time, the alternative hypothesis should indicate that the average personal time of women is greater than that of men, so H A: μ1 -μ2 > 0 is the correct choice.

Question 2

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.

Accepted Answer

A one-tailed paired t-test is appropriate because the data involves comparing the times (before and after implementing a standard work procedure) for the same group of employees, indicating paired observations, and the hypothesis specifically looks for a reduction (not just any difference) in time, which suggests a one-tailed test.

Question 3

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.

Accepted Answer

The formula for the degrees of freedom for a pooled t-test is (n1-1)+(n2-1), where n1 and n2 are the sample sizes of the two groups being compared. In this case, n1=16 and n2=20, so the degrees of freedom are (16-1)+(20-1)=34. Therefore, the correct answer is B) 34.

Question 4

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

Accepted Answer

The answer of A mid-sized company has decided to implement...

Question 5

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

Accepted Answer

The paired t-test is specifically designed for analyzing two sets of dependent or paired data, so the independent groups assumption is not relevant. The other assumptions/conditions listed are necessary for the validity of the test.

Question 6

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.

Accepted Answer

DA one-tailed paired t-test is appropriate because the hypothesis specifically predicts the direction of the effect (a decrease in anxiety levels) and involves comparing the same group of employees before and after the workshop. A two-tailed paired t-test could also be considered if the managers were interested in any change in anxiety levels, not just a decrease.

Question 7

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.

Accepted Answer

To find the pooled estimate of the variance, use the formula:

s^2pooled = [(n1-1)s1^2 + (n2-1)s2^2] / [n1 + n2 - 2]

where s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Plugging in the given values:

s1 = 2.84, n1 = 16
s2 = 2.75, n2 = 20

s^2pooled = [(16-1)(2.84)^2 + (20-1)(2.75)^2] / [16+20-2]
s^2pooled = (15*8.0656 + 19*7.5625) / 34
s^2pooled = 265.0624 / 34
s^2pooled = 7.788

Therefore, the answer is C) 7.785 (rounded to three decimal places).

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

Accepted Answer

The answer of Data were collected on annual personal time...

Question 9

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.

Accepted Answer

The confidence interval for the difference in means is calculated using the formula for the confidence interval of the difference between two independent means. Given the sample sizes, means, and standard deviations, the interval is calculated as 0.30 to 5.48 hours.

Question 10

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) $ \mu_{d}=0 $.
B) $ \mu_{d}<0 $.
C) $ \mu_{d}>0 $.
D) $ \mu_{d} \neq 0 $.
E) None of the above.

Accepted Answer

The alternative hypothesis $ \mu_{d}>0 $ suggests that the time required without the standard work procedure is greater than with it, indicating that the procedure reduces troubleshooting time.

Question 11

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) $ \mu_{d}=0 $
B) $ \mu_{d}<0 $
C) $ \mu_{d}>0 $
D) $ \mu_{d} \neq 0 $
E) $ \mu_{d} \leq 0 $

Accepted Answer

The alternative hypothesis should reflect the goal of the workshop, which is to decrease anxiety levels. If the approach was successful, we would expect the post-workshop anxiety level to be lower than the pre-workshop anxiety level, indicating a negative difference (d) value. Therefore, the correct alternative hypothesis is $ \mu_{d}<0 $.

Question 12

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. 
A)25.105
B)2.307
C)0.529
D)4.3589
E)None of the above.

Accepted Answer

The answer of An army depot that overhauls ground mobile...

Question 13

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.

Accepted Answer

Women and men are independent samples as they are not related or dependent on each other in terms of personal time taken. Therefore, the appropriate test in this situation is the t-test for two means for independent samples.

Quiz 12: Comparing Two Groups

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