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While in college student athletes can compete for four seasons in each sport. Due to the maturing of bodies and skill set, and more experience, it is often the case that the playing time of student athletes increases from their first year of participation until their fourth year of participation. Suppose population 1 is all female volleyball players in their fourth year of competition, and population 2 is all female volleyball players in their first year of competition. Of interest is to estimate the difference in the mean number of sets played by all female volleyball players in their fourth year of competition and the mean number of sets played by all female volleyball players in their first year of competition. A simple random sample of 8 female volleyball players in their fourth year of competition is selected, and the number of sets they played in their fourth year and the number of sets they played in their first year were recorded. The data is as follows. It is known that the population of differences in the number of sets played in the fourth and first years is normally distributed. If appropriate, use this information to test the hypotheses stated in question 8 at the a = .05 level of significance. Standard Deviation Student Fourth year First year Difference 2 1 61 54 23 51 38 3 3485 4 49 5 92 75 34 15 17 6 69 48 21 1255 7 72 17 8 96 84 12 Mean 72.00 47.50 24.50 17.24 23.34 16.90

While in college student athletes can compete for four seasons in each sport. Due to the maturing of bodies and skill set, and more experience, it is often the case that the playing time of student athletes increases from their first year of participation until their fourth year of participation. Suppose population 1 is all female volleyball players in their fourth year of competition, and population 2 is all female volleyball players in their first year of competition. Of interest is to estimate the difference in the mean number of sets played by all female volleyball players in their fourth year of competition and the mean number of sets played by all female volleyball players in their first year of competition. A simple random sample of 8 female volleyball players in their fourth year of competition is selected, and the number of sets they played in their fourth year and the number of sets they played in their first year were recorded. The data is as follows. It is known that the population of differences in the number of sets played in the fourth and first years is normally distributed. If appropriate, use this information to test the hypotheses stated in question 8 at the a = .05 level of significance. Standard Deviation Student Fourth year First year Difference 2 1 61 54 23 51 38 3 3485 4 49 5 92 75 34 15 17 6 69 48 21 1255 7 72 17 8 96 84 12 Mean 72.00 47.50 24.50 17.24 23.34 16.90

MATLAB: An Introduction with Applications
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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What is the p-value for the test statistic?
A) 0.0165
B) 0.0188803968
C) 0.168
D) 0.0085
E) 0.0022854202

### Analysis of Volleyball Players' Performance Over Their Collegiate Careers **Overview:** In college sports, student-athletes have the opportunity to compete across four seasons. As athletes mature physically and develop their skills further through experience, it is generally observed that their playing time increases from their first year to their fourth year. This study focuses on comparing the number of sets played by female volleyball players in their first and fourth years of competition. **Population Definitions:** - **Population 1:** All female volleyball players in their fourth year of competition. - **Population 2:** All female volleyball players in their first year of competition. **Objective:** The main goal is to estimate the difference in the mean number of sets played by all female volleyball players in their fourth year compared to their first year. **Methodology:** A simple random sample of 8 female volleyball players was selected. For each player, the number of sets played in their first and fourth years were recorded. The data collected is assumed to follow a normal distribution. **Data:** The table below presents the number of sets played by each student in their first and fourth years, including the respective means and standard deviations. | Student | Fourth Year | First Year | Difference | |---------|-------------|------------|------------| | 1 | 61 | 23 | 38 | | 2 | 54 | 51 | 3 | | 3 | 83 | 48 | 35 | | 4 | 49 | 34 | 15 | | 5 | 92 | 75 | 17 | | 6 | 69 | 48 | 21 | | 7 | 72 | 17 | 55 | | 8 | 96 | 84 | 12 | | | Mean | Standard Deviation | |----------|------------|---------------------| | Fourth year | 72.00 | 17.24 | | First year | 47.50 | 23.34 | | Difference | 24.50 | 16.90 | **Interpreting the Data:** - **Mean Values:** Athletes in their fourth year played more sets (mean of 72.00) compared to their first year (mean of 47
Transcribed Image Text:### Analysis of Volleyball Players' Performance Over Their Collegiate Careers **Overview:** In college sports, student-athletes have the opportunity to compete across four seasons. As athletes mature physically and develop their skills further through experience, it is generally observed that their playing time increases from their first year to their fourth year. This study focuses on comparing the number of sets played by female volleyball players in their first and fourth years of competition. **Population Definitions:** - **Population 1:** All female volleyball players in their fourth year of competition. - **Population 2:** All female volleyball players in their first year of competition. **Objective:** The main goal is to estimate the difference in the mean number of sets played by all female volleyball players in their fourth year compared to their first year. **Methodology:** A simple random sample of 8 female volleyball players was selected. For each player, the number of sets played in their first and fourth years were recorded. The data collected is assumed to follow a normal distribution. **Data:** The table below presents the number of sets played by each student in their first and fourth years, including the respective means and standard deviations. | Student | Fourth Year | First Year | Difference | |---------|-------------|------------|------------| | 1 | 61 | 23 | 38 | | 2 | 54 | 51 | 3 | | 3 | 83 | 48 | 35 | | 4 | 49 | 34 | 15 | | 5 | 92 | 75 | 17 | | 6 | 69 | 48 | 21 | | 7 | 72 | 17 | 55 | | 8 | 96 | 84 | 12 | | | Mean | Standard Deviation | |----------|------------|---------------------| | Fourth year | 72.00 | 17.24 | | First year | 47.50 | 23.34 | | Difference | 24.50 | 16.90 | **Interpreting the Data:** - **Mean Values:** Athletes in their fourth year played more sets (mean of 72.00) compared to their first year (mean of 47
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