MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Which of the following is the appropriate conclusion?
A) There is insufficient evidence that the mean number of sets they played in their fourth year of competition is higher than the mean number of sets they played in their first year of competition.


B) There is sufficient evidence that the mean number of sets they played in their fourth year of competition is higher than the mean number of sets they played in their first year of competition.


C) There is sufficient evidence that the mean number of sets they played in their fourth year of competition is the same as the mean number of sets theyplayed in their first year of competition.


D) There is sufficient evidence that the mean number of sets they played in their fourth year of competition is the same as the mean number of sets they played in their first year of competition.

### Analysis of Projection of Volleyball Sets Played by College Female Athletes from First to Fourth Year

#### Introduction
In collegiate sports, student athletes typically compete for up to four seasons. With increasing physical maturity, skill development, and experience over the years, it is not unusual for the amount of playing time to increment as athletes progress from their first to their fourth year. This analysis is focused on female volleyball players, investigating the mean difference in the number of sets played between athletes in their first year and those in their fourth year of competition.

#### Objectives
- **Population 1:** All female volleyball players in their fourth year.
- **Population 2:** All female volleyball players in their first year.
- **Goal:** Estimate the difference in the mean number of sets played by female volleyball players in their first and fourth years.

#### Data Collection Method
A simple random sample of 8 female volleyball players in their fourth year and the corresponding number of sets played in their first year were recorded:

| Student  | 1  | 2  | 3  | 4  | 5  | 6  | 7  | 8   |
|----------|----|----|----|----|----|----|----|-----|
| Fourth Year | 61 | 54 | 83 | 49 | 92 | 69 | 72 | 96  |
| First Year | 23 | 51 | 48 | 34 | 75 | 48 | 17 | 84  |
| Difference | 38 | 3  | 35 | 15 | 17 | 21 | 55 | 12  |

#### Statistical Summaries
- **Fourth Year:**
  - **Mean:** 72.00
  - **Standard Deviation:** 17.24
- **First Year:**
  - **Mean:** 47.50
  - **Standard Deviation:** 23.34
- **Difference:**
  - **Mean:** 24.50
  - **Standard Deviation:** 16.90

The differences in the number of sets played between the fourth and first years are assumed to be normally distributed. 

#### Hypothesis Testing
To analyze the significance of the mean difference between the fourth and first year, proceed with hypothesis testing at the 0.05 level of significance as prompted. This testing derives from examining the provided means and standard deviations.

#### Graph
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Transcribed Image Text:### Analysis of Projection of Volleyball Sets Played by College Female Athletes from First to Fourth Year #### Introduction In collegiate sports, student athletes typically compete for up to four seasons. With increasing physical maturity, skill development, and experience over the years, it is not unusual for the amount of playing time to increment as athletes progress from their first to their fourth year. This analysis is focused on female volleyball players, investigating the mean difference in the number of sets played between athletes in their first year and those in their fourth year of competition. #### Objectives - **Population 1:** All female volleyball players in their fourth year. - **Population 2:** All female volleyball players in their first year. - **Goal:** Estimate the difference in the mean number of sets played by female volleyball players in their first and fourth years. #### Data Collection Method A simple random sample of 8 female volleyball players in their fourth year and the corresponding number of sets played in their first year were recorded: | Student | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |----------|----|----|----|----|----|----|----|-----| | Fourth Year | 61 | 54 | 83 | 49 | 92 | 69 | 72 | 96 | | First Year | 23 | 51 | 48 | 34 | 75 | 48 | 17 | 84 | | Difference | 38 | 3 | 35 | 15 | 17 | 21 | 55 | 12 | #### Statistical Summaries - **Fourth Year:** - **Mean:** 72.00 - **Standard Deviation:** 17.24 - **First Year:** - **Mean:** 47.50 - **Standard Deviation:** 23.34 - **Difference:** - **Mean:** 24.50 - **Standard Deviation:** 16.90 The differences in the number of sets played between the fourth and first years are assumed to be normally distributed. #### Hypothesis Testing To analyze the significance of the mean difference between the fourth and first year, proceed with hypothesis testing at the 0.05 level of significance as prompted. This testing derives from examining the provided means and standard deviations. #### Graph
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