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ump to level 1 ompany would like to know if efficiency can be improved through a training course for employees. A sample of ployees is taken. The time taken for an employee to complete a task before training and after training is observed. After Before 33.1 n ance 16.81 ervations 30 othesized Mean Difference 0 29 at -2.282 <=t) one-tail 0.051 P= Ex: 1.234 ritical one-tail -1.699 <=t) two-tail 0.025 Critical two-tail -2.045 enfidence Level 95% -3 -2 -1 0 1 2 3 t=2.282 = 2 = 30 Degrees of freedom: df = 29 Point estimate for before training: 1 33.1 Point estimate for after training: ₂ 31.7 31.7 12.25 30 E

ump to level 1 ompany would like to know if efficiency can be improved through a training course for employees. A sample of ployees is taken. The time taken for an employee to complete a task before training and after training is observed. After Before 33.1 n ance 16.81 ervations 30 othesized Mean Difference 0 29 at -2.282 <=t) one-tail 0.051 P= Ex: 1.234 ritical one-tail -1.699 <=t) two-tail 0.025 Critical two-tail -2.045 enfidence Level 95% -3 -2 -1 0 1 2 3 t=2.282 = 2 = 30 Degrees of freedom: df = 29 Point estimate for before training: 1 33.1 Point estimate for after training: ₂ 31.7 31.7 12.25 30 E

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section: Chapter Questions
Problem 25SGR
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### Evaluating the Impact of Employee Training on Task Completion Efficiency #### Introduction A company seeks to determine if a training course can enhance the efficiency of its employees. To assess this, a sample of employees was observed, measuring the time taken to complete a specific task before and after the training session. #### Data Summary The following table reflects the statistical comparison of task completion times before and after training: | | **Before** | **After** | |-----------------------|------------|-----------| | **Mean** | 33.1 | 31.7 | | **Variance** | 16.81 | 12.25 | | **Observations** | 30 | 30 | | **Hypothesized Mean Difference** | 0 | | | **Degrees of Freedom (df)** | 29 | | | **t Stat** | -2.282 | | | **P(T<=t) one-tail** | 0.0151 | | | **t Critical one-tail** | -1.699 | | | **P(T<=t) two-tail** | 0.025 | | | **t Critical two-tail** | -2.045 | | | **Confidence Level** | 95% | | #### Key Statistical Values - **Sample Size (n):** 30 - **Degrees of Freedom (df):** 29 - **Point Estimate for Mean Before Training (\( \bar{x}_1 \)):** 33.1 - **Point Estimate for Mean After Training (\( \bar{x}_2 \)):** 31.7 #### Graphical Representation The included graph is a t-distribution curve representing the calculated t-statistic. The curve is centered at zero and extends symmetrically in both directions, signifying the distribution of possible values of the t-statistic. - **t-statistic (highlighted):** -2.282 - **Critical t-values for one-tail and two-tail tests:** -1.699 and -2.045, respectively. The shaded region under the curve represents the significance level for one-tail (0.0151) and two-tail (0.025) tests. #### Conclusion Based on the calculated t-statistic and the corresponding p-values, we can infer the effectiveness of the training program on employees
Transcribed Image Text:### Evaluating the Impact of Employee Training on Task Completion Efficiency #### Introduction A company seeks to determine if a training course can enhance the efficiency of its employees. To assess this, a sample of employees was observed, measuring the time taken to complete a specific task before and after the training session. #### Data Summary The following table reflects the statistical comparison of task completion times before and after training: | | **Before** | **After** | |-----------------------|------------|-----------| | **Mean** | 33.1 | 31.7 | | **Variance** | 16.81 | 12.25 | | **Observations** | 30 | 30 | | **Hypothesized Mean Difference** | 0 | | | **Degrees of Freedom (df)** | 29 | | | **t Stat** | -2.282 | | | **P(T<=t) one-tail** | 0.0151 | | | **t Critical one-tail** | -1.699 | | | **P(T<=t) two-tail** | 0.025 | | | **t Critical two-tail** | -2.045 | | | **Confidence Level** | 95% | | #### Key Statistical Values - **Sample Size (n):** 30 - **Degrees of Freedom (df):** 29 - **Point Estimate for Mean Before Training (\( \bar{x}_1 \)):** 33.1 - **Point Estimate for Mean After Training (\( \bar{x}_2 \)):** 31.7 #### Graphical Representation The included graph is a t-distribution curve representing the calculated t-statistic. The curve is centered at zero and extends symmetrically in both directions, signifying the distribution of possible values of the t-statistic. - **t-statistic (highlighted):** -2.282 - **Critical t-values for one-tail and two-tail tests:** -1.699 and -2.045, respectively. The shaded region under the curve represents the significance level for one-tail (0.0151) and two-tail (0.025) tests. #### Conclusion Based on the calculated t-statistic and the corresponding p-values, we can infer the effectiveness of the training program on employees
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