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#### IntroductionIn 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 MethodA 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:** 16.90The differences in the number of sets played between the fourth and first years are assumed to be normally distributed. #### Hypothesis TestingTo 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

Given data : sample size( n) =8 sample mean( d) = 24.50 where d denotes the differences…

Answered: Which of the following is the…

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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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

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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