### Matched-Pairs Hypothesis Test for Completion Time with Ear BudsA manager wishes to see if the time (in minutes) it takes for their workers to complete a certain task will increase when they are allowed to wear ear buds at work. A random sample of 9 workers' times were collected before and after wearing ear buds. Assume the data is normally distributed. Perform a Matched-Pairs hypothesis test for the claim that the time to complete the task has increased at a significance level of $ \alpha = 0.01 $.If you wish to copy this data to a spreadsheet or StatCrunch, you may find it useful to first copy it to Notepad, in order to remove any formatting.Round answers to 4 decimal places.For the context of this problem,\[ \mu_d = \mu_{After} - \mu_{Before} \]where the first data set represents "after" and the second data set represents "before".Hypotheses:\[ H_0: \mu_d = 0 \]\[ H_a: \mu_d > 0 \]### Sample Data| After | Before ||---------|---------|| 71.9 | 51.7 || 39.1 | 39.2 || 51 | 52.1 || 54.7 | 55.8 || 54.1 | 50.5 || 46.9 | 43.2 || 45.1 | 34.2 || 63.4 | 54.9 || 57.1 | 41.1 |### Questions1. **What is the mean difference for this sample?** - Mean difference = ___________2. **What is the significance level for this sample?** - Significance level = ___________3. **What is the P-value for this test?** - P-value = ___________### Explanation of Sample Data TableThe sample data is organized into two columns: "After" and "Before," representing the completion times (in minutes) of workers after and before wearing ear buds, respectively. Each row corresponds to a different worker's times. There are 9 pairs of data points

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A manager wishes to see if the time (in minutes) it takes for their workers to complete a certain task will increase when they are allowed to wear ear buds at work. A random sample of 9 workers' times were collected before and after wearing ear buds. Assume the data is normally distributed. Perform a Matched-Pairs hypothesis test for the claim that the time to complete the task has increased at a significance level of a = 0.01. If you wish to copy this data to a spreadsheet or StatCrunch, you may find it useful to first copy it to Notepad, in order to remove any formatting. Round answers to 4 decimal places. For the context of this problem, µa = Hafter · H_Before, where the first data set represents "after" and the second data set represents "before". H.:µd = 0 0 < Prl :®H

A manager wishes to see if the time (in minutes) it takes for their workers to complete a certain task will increase when they are allowed to wear ear buds at work. A random sample of 9 workers' times were collected before and after wearing ear buds. Assume the data is normally distributed. Perform a Matched-Pairs hypothesis test for the claim that the time to complete the task has increased at a significance level of a = 0.01. If you wish to copy this data to a spreadsheet or StatCrunch, you may find it useful to first copy it to Notepad, in order to remove any formatting. Round answers to 4 decimal places. For the context of this problem, µa = Hafter · H_Before, where the first data set represents "after" and the second data set represents "before". H.:µd = 0 0 < Prl :®H

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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### Matched-Pairs Hypothesis Test for Completion Time with Ear Buds

A manager wishes to see if the time (in minutes) it takes for their workers to complete a certain task will increase when they are allowed to wear ear buds at work. A random sample of 9 workers' times were collected before and after wearing ear buds. Assume the data is normally distributed.

Perform a Matched-Pairs hypothesis test for the claim that the time to complete the task has increased at a significance level of $ \alpha = 0.01 $.

If you wish to copy this data to a spreadsheet or StatCrunch, you may find it useful to first copy it to Notepad, in order to remove any formatting.

Round answers to 4 decimal places.

For the context of this problem,
\[ \mu_d = \mu_{After} - \mu_{Before} \]

where the first data set represents "after" and the second data set represents "before".

Hypotheses:
\[ H_0: \mu_d = 0 \]
\[ H_a: \mu_d > 0 \]

### Sample Data

| After | Before |
|---------|---------|
| 71.9 | 51.7 |
| 39.1 | 39.2 |
| 51 | 52.1 |
| 54.7 | 55.8 |
| 54.1 | 50.5 |
| 46.9 | 43.2 |
| 45.1 | 34.2 |
| 63.4 | 54.9 |
| 57.1 | 41.1 |

### Questions

1. **What is the mean difference for this sample?**
- Mean difference = ___________

2. **What is the significance level for this sample?**
- Significance level = ___________

3. **What is the P-value for this test?**
- P-value = ___________

### Explanation of Sample Data Table

The sample data is organized into two columns: "After" and "Before," representing the completion times (in minutes) of workers after and before wearing ear buds, respectively. Each row corresponds to a different worker's times. There are 9 pairs of data points

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