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. 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 theplaying time of student athletes increases from their first year of participation until their fourth year of participation. Suppose population 1 is all female volleyball playersin 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 meannumber 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 firstyear 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 numberof 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 andfirst 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 DeviationStudentFourth yearFirst yearDifference12615423 51383383483544934155927517669482177217558968412Mean72.0047.5024.5017.2423.3416.90

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

Answered: Which of the following is the…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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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.

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
1
2
61
54
23 51
38
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
72.00
47.50
24.50
17.24
23.34
16.90

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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