calculate the Sd.
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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calculate the Sd.
![### Analysis of Pass Completion Percentages of College Football Quarterbacks: Freshman vs. Sophomore Seasons
This educational webpage details the statistical analysis of pass completion percentages for 10 college football quarterbacks during their freshman and sophomore seasons. We will determine whether there is sufficient evidence to claim that the pass completion percentages have changed from one season to the next at a significance level of α = 0.01.
#### Data Table
| Player | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|--------|------|------|------|------|------|------|------|------|------|------|
| **Completion percentage (freshman)** | 68.5 | 62.7 | 56.3 | 61.0 | 62.8 | 52.0 | 56.0 | 62.5 | 53.9 | 57.3 |
| **Completion percentage (sophomore)** | 68.3 | 56.7 | 62.5 | 62.5 | 61.1 | 59.6 | 61.3 | 61.5 | 55.8 | 58.6 |
#### Statistical Hypothesis Testing
To establish whether the pass completion percentages have significantly changed, we propose and examine the following hypothesis:
##### (a) Hypotheses
- \( H_0: \mu_d = 0 \) (Null hypothesis: There is no difference in mean pass completion percentages between freshman and sophomore seasons.)
- \( H_a: \mu_d \neq 0 \) (Alternative hypothesis: There is a difference in mean pass completion percentages between freshman and sophomore seasons.)
The correct hypothesis test selection is indicated by option **E**.
##### (b) Calculation of Sample Mean Difference (\(\bar{d}\)) and Standard Deviation of Differences (\(s_d\))
###### Calculate \(\bar{d}\)
The sample mean difference \(\bar{d}\) is calculated as:
\[ \bar{d} = -1.490 \]
(Rounded to three decimal places.)
###### Calculate \(s_d\)
The standard deviation of the differences \(s_d\) needs to be calculated and rounded to three decimal places:
\[ s_d = 2.905 \]
### Conclusion
Based on these](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7c71094c-6a42-4b2e-b93a-0f0d489253a3%2F3359462a-ad08-4cfd-bb90-1d18acf587f9%2F9fhk2ml_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Analysis of Pass Completion Percentages of College Football Quarterbacks: Freshman vs. Sophomore Seasons
This educational webpage details the statistical analysis of pass completion percentages for 10 college football quarterbacks during their freshman and sophomore seasons. We will determine whether there is sufficient evidence to claim that the pass completion percentages have changed from one season to the next at a significance level of α = 0.01.
#### Data Table
| Player | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|--------|------|------|------|------|------|------|------|------|------|------|
| **Completion percentage (freshman)** | 68.5 | 62.7 | 56.3 | 61.0 | 62.8 | 52.0 | 56.0 | 62.5 | 53.9 | 57.3 |
| **Completion percentage (sophomore)** | 68.3 | 56.7 | 62.5 | 62.5 | 61.1 | 59.6 | 61.3 | 61.5 | 55.8 | 58.6 |
#### Statistical Hypothesis Testing
To establish whether the pass completion percentages have significantly changed, we propose and examine the following hypothesis:
##### (a) Hypotheses
- \( H_0: \mu_d = 0 \) (Null hypothesis: There is no difference in mean pass completion percentages between freshman and sophomore seasons.)
- \( H_a: \mu_d \neq 0 \) (Alternative hypothesis: There is a difference in mean pass completion percentages between freshman and sophomore seasons.)
The correct hypothesis test selection is indicated by option **E**.
##### (b) Calculation of Sample Mean Difference (\(\bar{d}\)) and Standard Deviation of Differences (\(s_d\))
###### Calculate \(\bar{d}\)
The sample mean difference \(\bar{d}\) is calculated as:
\[ \bar{d} = -1.490 \]
(Rounded to three decimal places.)
###### Calculate \(s_d\)
The standard deviation of the differences \(s_d\) needs to be calculated and rounded to three decimal places:
\[ s_d = 2.905 \]
### Conclusion
Based on these
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