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
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question

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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