Exam 12: Comparing Two Means

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? Without Standard Work Procedure With Standard Work Procedure Difference Without - With 142 119 23 144 118 26 153 126 27 148 119 29 146 121 25 149 125 24 138 116 22 145 120 25 153 124 29 160 138 22 163 135 28 170 144 26 169 142 27 151 128 23 152 131 21 167 141 26 164 140 24 165 140 25 163 138 25 -Are the assumptions and conditions for carrying out the paired t-test satisfied? Explain.

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

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

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

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

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

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? Pre-workshop anxiety level 7 6 9 5 6 7 5 7 6 4 3 2 1 3 4 2 Post-workshop anxiety level 4 3 7 3 4 5 4 6 5 3 2 2 1 3 4 3 Difference (Post - Pre) -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 0 1 Determine whether two samples are independent or paired. -Create and interpret a 90% confidence interval.

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

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

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

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? Pre-workshop anxiety level 7 6 9 5 6 7 5 7 6 4 3 2 1 3 4 2 Post-workshop anxiety level 4 3 7 3 4 5 4 6 5 3 2 2 1 3 4 3 Difference (Post - Pre) -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 0 1 Determine whether two samples are independent or paired. -Write the null and alternative hypotheses.

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 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

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

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 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 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? Pre-workshop anxiety level 7 6 9 5 6 7 5 7 6 4 3 2 1 3 4 2 Post-workshop anxiety level 4 3 7 3 4 5 4 6 5 3 2 2 1 3 4 3 Difference (Post - Pre) -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 0 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

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

Write the null and alternative hypotheses.