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Wisconsin State government is attempting to improve the productivity of its workforce by trying to reduce the number of productive hours lost due to clerical mistakes. Wisconsin government plans to install new software to help manage productivity and reduce number of hours lost. To test the effectiveness of this software, a random sample of 50 departments across the state have been selected. For each of the 50 departments, number of hours lost in productivity is recorded in the month before and the month after the installation of the new software. For each department in the sample percentage change was calculated and then averaged across all the departments. Based on this sample, the average percentage change was calculated to be -1.20%. Assume that the population standard deviation is o = 6. Can it be inferred at the 10% significance level that the new software is effective at reducing loss of productive hours? (Hint: here u = the mean percentage change; and sample mean is -1.2)

Wisconsin State government is attempting to improve the productivity of its workforce by trying to reduce the number of productive hours lost due to clerical mistakes. Wisconsin government plans to install new software to help manage productivity and reduce number of hours lost. To test the effectiveness of this software, a random sample of 50 departments across the state have been selected. For each of the 50 departments, number of hours lost in productivity is recorded in the month before and the month after the installation of the new software. For each department in the sample percentage change was calculated and then averaged across all the departments. Based on this sample, the average percentage change was calculated to be -1.20%. Assume that the population standard deviation is o = 6. Can it be inferred at the 10% significance level that the new software is effective at reducing loss of productive hours? (Hint: here u = the mean percentage change; and sample mean is -1.2)

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section: Chapter Questions
Problem 8CR
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#20)

- State the null and alternative hypothesis

- What is the test statistic?

-What is the P-value?

-What is the conclusion of the test?

Wisconsin State government is attempting to improve the productivity of its workforce by trying to reduce the number of productive hours lost due to clerical mistakes. Wisconsin government plans to install new software to help manage productivity and reduce number of hours lost. To test the effectiveness of this software, a random sample of 50 departments across the state have been selected. For each of the 50 departments, number of hours lost in productivity is recorded in the month before and the month after the installation of the new software. For each department in the sample percentage change was calculated and then averaged across all the departments. Based on this sample, the average percentage change was calculated to be -1.20%. Assume that the population standard deviation is o = 6. Can it be inferred at the 10% significance level that the new software is effective at reducing loss of productive hours? (Hint: here µ = the mean percentage change; and sample mean is -1.2)
Transcribed Image Text:Wisconsin State government is attempting to improve the productivity of its workforce by trying to reduce the number of productive hours lost due to clerical mistakes. Wisconsin government plans to install new software to help manage productivity and reduce number of hours lost. To test the effectiveness of this software, a random sample of 50 departments across the state have been selected. For each of the 50 departments, number of hours lost in productivity is recorded in the month before and the month after the installation of the new software. For each department in the sample percentage change was calculated and then averaged across all the departments. Based on this sample, the average percentage change was calculated to be -1.20%. Assume that the population standard deviation is o = 6. Can it be inferred at the 10% significance level that the new software is effective at reducing loss of productive hours? (Hint: here µ = the mean percentage change; and sample mean is -1.2)
e. The State Controller is concerned that the test was not sensitive enough to detect small but import changes. The Controller worries that if the true reduction in time lost to clerical mistakes is actually 2% (that is, µ = - 2), then the state may miss the opportunity to install very effective software. Find the probability that the test with o = 6, a = .10, 50 will fail to conclude that such software is effective. and n = Answer for e: 1423
Transcribed Image Text:e. The State Controller is concerned that the test was not sensitive enough to detect small but import changes. The Controller worries that if the true reduction in time lost to clerical mistakes is actually 2% (that is, µ = - 2), then the state may miss the opportunity to install very effective software. Find the probability that the test with o = 6, a = .10, 50 will fail to conclude that such software is effective. and n = Answer for e: 1423
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