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Exam 14: Comparing Two Groups

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Question 1

Multiple Choice

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Check assumptions / conditions for the paired t-test. -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

F) B) and D)
G) A) and B)

Correct Answer

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B

Question 2

Multiple Choice

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Create a confidence interval for the difference between two means. -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.

F) C) and D)
G) A) and E)

Correct Answer

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A

Question 3

Multiple Choice

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Apply the paired t-test. -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

Apply the pooled t-test. -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

Calculate the standard error for the mean difference. -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 standard error of the mean difference is $\begin{array} { | c | c | c | } \hline \begin{array} { c } \text { Without } \\\text { Standard } \\\text { Work } \\\text { Procedure }\end{array} & \begin{array} { c } \text { With Standard } \\\text { Work } \\\text { Procedure }\end{array} & \begin{array} { c } \text { Difference } \\\text { Without - } \\\text { With }\end{array} \\\hline 142 & 119 & 23 \\\hline 144 & 118 & 26 \\\hline 153 & 126 & 27 \\\hline 148 & 119 & 29 \\\hline 146 & 121 & 25 \\\hline 149 & 125 & 24 \\\hline 138 & 116 & 22 \\\hline 145 & 120 & 25 \\\hline 153 & 124 & 29 \\\hline 160 & 138 & 22 \\\hline 163 & 135 & 28 \\\hline 170 & 144 & 26 \\\hline 169 & 142 & 27 \\\hline 151 & 128 & 23 \\\hline 152 & 131 & 21 \\\hline 167 & 141 & 26 \\\hline 164 & 140 & 24 \\\hline 165 & 140 & 25 \\\hline 163 & 138 & 25 \\\hline\end{array}$

Write hypotheses for the two-sample t-test. -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. $H _ { 0 : } \mu _ { 1 } - \mu _ { 2 } = 0$ and $H _ { \mathrm { A } : } \mu _ { 1 } - \mu _ { 2 } \neq 0$ . 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.

Create a confidence interval for the mean difference. -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? $\begin{array} { | l | c | c | c | c | c | c | c | c | c | c | c | c | c | c | c | c | } \hline \begin{array} { l } \text { Pre-workshop } \\\text { anxiety level }\end{array} & 7 & 6 & 9 & 5 & 6 & 7 & 5 & 7 & 6 & 4 & 3 & 2 & 1 & 3 & 4 & 2 \\\hline \begin{array} { l } \text { Post-workshop } \\\text { anxiety level }\end{array} & 4 & 3 & 7 & 3 & 4 & 5 & 4 & 6 & 5 & 3 & 2 & 2 & 1 & 3 & 4 & 3 \\\hline \begin{array} { l } \text { Difference } \\\text { (Post - Pre) }\end{array} & - 3 & - 3 & - 2 & - 2 & - 2 & - 2 & - 1 & - 1 & - 1 & - 1 & - 1 & 0 & 0 & 0 & 0 & 1 \\\hline\end{array}$

Analyze a conclusion using standardized residuals. -Are the assumptions and conditions for carrying out the paired t-test satisfied? Explain.

Write hypotheses for the two-sample t-test. -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. $\mathrm { H } _ { 0 } : \mu _ { \mathrm { A } } - \mu _ { \mathrm { B } } = 0$ and $\mathrm { H } _ { \mathrm { A } } : \mu _ { \mathrm { A } } - \mu _ { \mathrm { B } } < 0$ B. $\mathrm { H } _ { 0 : } \mu _ { \mathrm { A } } - \mu _ { \mathrm { B } } = 0$ and $\mathrm { H } _ { \mathrm { A } : } \mu _ { \mathrm { A } } - \mu _ { \mathrm { B } } \neq 0$ . C. $H _ { 0 : } \mu _ { \mathrm { A } } - \mu _ { \mathrm { B } } = 0$ and $\mathrm { H } _ { \mathrm { A } : } \mu _ { \mathrm { A } } - \mu _ { \mathrm { B } } > 0$ . D. $\mathrm { H } _ { 0 : } \mu _ { \mathrm { A } } - \mu _ { \mathrm { B } } > 0$ and $\mathrm { H } _ { \mathrm { A } : } \mu _ { \mathrm { A } } - \mu _ { \mathrm { B } } < 0$ . E. None of the above.

Apply the pooled t-test. -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

Analyze a conclusion using standardized residuals. -Create and interpret a 90% confidence interval.

Analyze a conclusion using standardized residuals. -Are the assumptions and conditions for carrying out the t-test for two means satisfied? Explain.

Calculate the standard error for the difference between two independent means. -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

Write hypotheses for the paired t-test. -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. $\mu _ { d } \leq 0$

Analyze a conclusion using standardized residuals. -Create and interpret a 90% confidence interval.

Analyze a conclusion using standardized residuals. -Create and interpret a 95% confidence interval.

Apply the paired t-test. -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

Write hypotheses for the paired t-test. -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.

Check assumptions / conditions for two-sample t-test. -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