Introduction to the Practice of Statistics: w/CrunchIt/EESEE Access Card
Introduction to the Practice of Statistics: w/CrunchIt/EESEE Access Card
8th Edition
ISBN: 9781464158933
Author: David S. Moore, George P. McCabe, Bruce A. Craig
Publisher: W. H. Freeman
bartleby

Concept explainers

bartleby

Videos

Question
Book Icon
Chapter 2.4, Problem 70E

(a)

To determine

To find: The comparison of two predicted mean strengths using their difference.

(a)

Expert Solution
Check Mark

Answer to Problem 70E

Solution: The predicted dominant arm strength for a baseball player is 5.138 units more than the non-baseball player.

Explanation of Solution

Calculation: It is noted from the referred Exercises 2.70 and 2.71 that the predicted mean strength of the dominant arm (y^1) is 17.716cm4/1000 for a non-baseball player and the predicted mean strength of the dominant arm (y^1) is 22.854cm4/1000 for a baseball player who uses exercise strength. In both the cases, the non-dominant arm strength is 16cm4/1000.

The difference in the two predicted mean strengths is calculated as:

y^2y^1={Mean arm strength for   a baseball player }{Mean arm strength for  a non-baseball player }=22.85417.716=5.138

Therefore, the difference in the mean strengths of a baseball and a non-baseball player is positive. This implies that the predicted dominant arm strength for a baseball player, who uses exercise strength, is greater than the predicted dominant arm strength for a baseball player, who uses control more than the exercise strength. Thus, it can be said that y^2>y^1.

(b)

To determine

To explain: The inference for the difference in the two predicted mean strengths.

(b)

Expert Solution
Check Mark

Answer to Problem 70E

Solution: There is a positive impact of the baseball throwing exercise over control as the difference in the mean arm strengths of the baseball player and a non-baseball player is positive.

Explanation of Solution

From the referred exercise, it is ascertained that the difference in the predicted arm strengths for a baseball and a non-baseball player is 5.138cm4/1000. The difference is positive for the same non-dominant arm strength as 16cm4/1000 in both the cases, implying that the mean arm strength for a baseball player is relatively more than the mean arm strength for a non-baseball player. It is also provided that the baseball player exercises baseball throwing practice while using the arm strength and a non-baseball player uses control more than the exercise. Hence, it can be said that the baseball throwing exercise has a positive impact and improves the strength of arm bones for a player.

(c)

Section 1

To determine

To find: The predicted dominant arm strengths for non-dominant strengths 12cm4/1000 and 20cm4/1000.

(c)

Section 1

Expert Solution
Check Mark

Answer to Problem 70E

Solution: The results obtained are represented in the following table:

Dominant arm Strength

Non-Baseball Player (cm4/1000)

Baseball Player (cm4/1000)

Non-Dominant Arm Strength

12cm4/1000

y^3=13.972

y^4=17.362

20cm4/1000

y^5=21.46

y^6=28.346

Explanation of Solution

Calculation: The linear regression equations for a non-baseball player is:

Dominant=2.74+(0.936×nondominant)

and for a baseball player is:

Dominant=0.886+(1.373×nondominant)

From the above part (a), the dominant arm strengths when the non-dominant strength is 16cm4/1000 are obtained as 17.716cm4/1000 for a non-baseball player and 22.854cm4/1000 for a baseball player.

The dominant arm strengths provided the non-dominant arm strength as 12cm4/1000 are calculated as follows:

For a non-baseball player, it is represented as y^3 and computed as:

Dominant=2.74+(0.936×nondominant)y^3=2.74+(0.936×12)y^3=13.972

For a baseball player, it is represented as y^4 and computed as:

Dominant=0.886+(1.373×nondominant)y^4=0.886+(1.373×12)y^4=17.362

The dominant arm strengths provided the non-dominant arm strength as 20cm4/1000 are calculated as follows:

For a non-baseball player, it is represented as y^5 and computed as:

Dominant=2.74+(0.936×nondominant)y^5=2.74+(0.936×20)y^5=21.46

For a baseball player, it is represented as y^6 and computed as:

Dominant=0.886+(1.373×nondominant)y^6=0.886+(1.373×20)y^6=28.346

The above results obtained can be represented in the form of a table as follows:

Dominant arm Strength

Non-Baseball Player (cm4/1000)

Baseball Player (cm4/1000)

Non-Dominant Arm Strength

12cm4/1000

y^3=13.972

y^4=17.362

20cm4/1000

y^5=21.46

y^6=28.346

Section 2:

To determine

To find: The differences in the respective arm strengths.

Section 2:

Expert Solution
Check Mark

Answer to Problem 70E

Solution: The differences are 3.39cm4/1000 for 12cm4/1000 and 6.886cm4/1000 for 20cm4/1000.

Explanation of Solution

Calculation: The arm strengths for the non-dominant arm strengths 12cm4/1000 and 20cm4/1000 are obtained from the above part as follows:

Dominant arm Strength

Non-Baseball Player (cm4/1000)

Baseball Player (cm4/1000)

Non-Dominant Arm Strength

12cm4/1000

y^3=13.972

y^4=17.362

20cm4/1000

y^5=21.46

y^6=28.346

The difference in the arm strengths of baseball and the non-baseball players are calculated as follows:

For non-dominant arm strength 12cm4/1000.

y^4y^3={Mean arm strength for   a baseball player }{Mean arm strength for  a non-baseball player }=17.36213.972=3.39

For non-dominant arm strength 20cm4/1000.

y^6y^5={Mean arm strength for   a baseball player }{Mean arm strength for  a non-baseball player }=28.34621.46=6.886cm4/1000

Hence, the differences are 3.39cm4/1000 for 12cm4/1000 and 6.886cm4/1000 for 20cm4/1000.

Section 3:

To determine

To find: A table for the results of the three calculations.

Section 3:

Expert Solution
Check Mark

Answer to Problem 70E

Solution: The resultant table is obtained as follows:

Dominant arm Strength

Non-Baseball Player (cm4/1000)

Baseball Player (cm4/1000)

Differences

Non-Dominant Arm Strength

12cm4/1000

y^3=13.972

y^4=17.362

y^4y^3=3.39

16cm4/1000

y^1=17.716

y^2=22.854

y^2y^1=5.138

20cm4/1000

y^5=21.46

y^6=28.346

y^6y^5=6.886

Explanation of Solution

From sections 1 and 2 of part (c) of exercise 2.72, the following values are obtained:

y^1=17.716cm4/1000

y^2=22.854cm4/1000

y^3=13.972

y^4=17.362

Also,

y^5=21.46

y^6=28.346

The differences in the estimated strengths have been calculated as:

y^2y^1=5.138cm4/1000

y^4y^3=3.39cm4/1000

y^6y^5=6.886cm4/1000

where, y^1, y^3, and y^5 represent the dominant arm strengths of the non-baseball players with non-dominant arm strengths as 16cm4/1000, 12cm4/1000, and 20cm4/1000, respectively, and y^2, y^4, and y^6 represent the dominant arm strengths of the baseball players with non-dominant arm strengths as 16cm4/1000, 12cm4/1000, and 20cm4/1000, respectively. The (y^2y^1), (y^4y^3), and (y^6y^5) represent the differences in the mean arm strengths of both the players for all the three cases.

The above information can be represented in the form of a table as follows:

Dominant arm Strength

Non-Baseball Player (cm4/1000)

Baseball Player (cm4/1000)

Differences

Non-Dominant Arm Strength

12cm4/1000

y^3=13.972

y^4=17.362

y^4y^3=3.39

16cm4/1000

y^1=17.716

y^2=22.854

y^2y^1=5.138

20cm4/1000

y^5=21.46

y^6=28.346

y^6y^5=6.886

(d)

Section 1:

To determine

To explain: The summary of results obtained in part (c) of exercise 2.72.

(d)

Section 1:

Expert Solution
Check Mark

Answer to Problem 70E

Solution: The results show that the baseball throwing exercise has resulted in an improvement in the dominant arm strengths of the baseball players as compared to the non-baseball players for all the three cases. That is, the difference between the two is positive for all the three cases.

Explanation of Solution

The results obtained in the above part are as follows:

Dominant arm Strength

Non-Baseball Player (cm4/1000)

Baseball Player (cm4/1000)

Difference

Non-Dominant Arm Strength

12cm4/1000

y^3=13.972

y^4=17.362

y^4y^3=3.39

16cm4/1000

y^1=17.716

y^2=22.854

y^2y^1=5.138

20cm4/1000

y^5=21.46

y^6=28.346

y^6y^5=6.886

From the table obtained, it is ascertained that the difference in the dominant arm strengths of baseball and the non-baseball players for all the three cases of non-dominant arm strengths as 16cm4/1000, 12cm4/1000, and 20cm4/1000 are positive. This implies that the baseball throwing exercise results in an improvement in the arm strengths of the players. Thus, the use of the baseball throwing exercise is more beneficial for the players than using the control exercise.

Section 2:

To determine

To explain: The reason for the non-similarity of the three differences obtained.

Section 2:

Expert Solution
Check Mark

Answer to Problem 70E

Solution: The non-similarity is due to a positive relation between the dominant arm strength and the non-dominant arm strength. The more the value of non-dominant arm strength, the more will be the dominant arm strength and hence, the greater will be the difference.

Explanation of Solution

The differences for all the three cases non-dominant arm strengths as 16cm4/1000, 12cm4/1000, and 20cm4/1000 are:

y^4y^3=3.39,

y^2y^1=5.138,and

y^6y^5=6.886,

respectively. The point to be noted here is that when the non-dominant arm strength increases, the value of the dominant arm strength also improves, thus, the difference in the dominant arm strengths of baseball and the non-baseball players also improves. That is, there is a positive relation amongst the non-dominant arm strength and the difference thus obtained. The more the value of non-dominant strength, the more will be the dominant strength and the more will be the difference between the two. That is why, there is a non-similarity of the differences in all the three cases.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Homework Let X1, X2, Xn be a random sample from f(x;0) where f(x; 0) = (-), 0 < x < ∞,0 € R Using Basu's theorem, show that Y = min{X} and Z =Σ(XY) are indep. -
Homework Let X1, X2, Xn be a random sample from f(x; 0) where f(x; 0) = e−(2-0), 0 < x < ∞,0 € R Using Basu's theorem, show that Y = min{X} and Z =Σ(XY) are indep.
An Arts group holds a raffle.  Each raffle ticket costs $2 and the raffle consists of 2500 tickets.  The prize is a vacation worth $3,000.    a. Determine your expected value if you buy one ticket.     b. Determine your expected value if you buy five tickets.     How much will the Arts group gain or lose if they sell all the tickets?

Chapter 2 Solutions

Introduction to the Practice of Statistics: w/CrunchIt/EESEE Access Card

Ch. 2.2 - Prob. 11UYKCh. 2.2 - Prob. 12UYKCh. 2.2 - Prob. 13UYKCh. 2.2 - Prob. 14UYKCh. 2.2 - Prob. 15UYKCh. 2.2 - Prob. 16UYKCh. 2.2 - Prob. 17UYKCh. 2.2 - Prob. 18ECh. 2.2 - Prob. 19ECh. 2.2 - Prob. 20ECh. 2.2 - Prob. 21ECh. 2.2 - Prob. 22ECh. 2.2 - Prob. 23ECh. 2.2 - Prob. 24ECh. 2.2 - Prob. 25ECh. 2.2 - Prob. 26ECh. 2.2 - Prob. 27ECh. 2.2 - Prob. 28ECh. 2.2 - Prob. 29ECh. 2.2 - Prob. 30ECh. 2.2 - Prob. 31ECh. 2.2 - Prob. 32ECh. 2.2 - Prob. 33ECh. 2.2 - Prob. 34ECh. 2.2 - Prob. 35ECh. 2.2 - Prob. 36ECh. 2.2 - Prob. 37ECh. 2.3 - Prob. 38UYKCh. 2.3 - Prob. 39UYKCh. 2.3 - Prob. 40ECh. 2.3 - Prob. 41ECh. 2.3 - Prob. 42ECh. 2.3 - Prob. 43ECh. 2.3 - Prob. 44ECh. 2.3 - Prob. 45ECh. 2.3 - Prob. 46ECh. 2.3 - Prob. 47ECh. 2.3 - Prob. 48ECh. 2.3 - Prob. 49ECh. 2.3 - Prob. 50ECh. 2.3 - Prob. 51ECh. 2.3 - Prob. 52ECh. 2.3 - Prob. 53ECh. 2.3 - Prob. 54ECh. 2.3 - Prob. 55ECh. 2.3 - Prob. 56ECh. 2.3 - Prob. 57ECh. 2.3 - Prob. 58ECh. 2.3 - Prob. 59ECh. 2.3 - Prob. 60ECh. 2.3 - Prob. 61ECh. 2.4 - Prob. 62UYKCh. 2.4 - Prob. 63UYKCh. 2.4 - Prob. 64UYKCh. 2.4 - Prob. 65UYKCh. 2.4 - Prob. 66ECh. 2.4 - Prob. 67ECh. 2.4 - Prob. 68ECh. 2.4 - Prob. 69ECh. 2.4 - Prob. 70ECh. 2.4 - Prob. 71ECh. 2.4 - Prob. 72ECh. 2.4 - Prob. 73ECh. 2.4 - Prob. 74ECh. 2.4 - Prob. 75ECh. 2.4 - Prob. 76ECh. 2.4 - Prob. 77ECh. 2.4 - Prob. 78ECh. 2.4 - Prob. 79ECh. 2.4 - Prob. 80ECh. 2.4 - Prob. 81ECh. 2.4 - Prob. 82ECh. 2.4 - Prob. 83ECh. 2.4 - Prob. 84ECh. 2.4 - Prob. 85ECh. 2.4 - Prob. 86ECh. 2.4 - Prob. 87ECh. 2.4 - Prob. 88ECh. 2.4 - Prob. 89ECh. 2.4 - Prob. 90ECh. 2.4 - Prob. 91ECh. 2.5 - Prob. 92UYKCh. 2.5 - Prob. 93UYKCh. 2.5 - Prob. 94ECh. 2.5 - Prob. 95ECh. 2.5 - Prob. 96ECh. 2.5 - Prob. 97ECh. 2.5 - Prob. 98ECh. 2.5 - Prob. 99ECh. 2.5 - Prob. 100ECh. 2.5 - Prob. 101ECh. 2.5 - Prob. 102ECh. 2.5 - Prob. 103ECh. 2.5 - Prob. 104ECh. 2.5 - Prob. 105ECh. 2.5 - Prob. 106ECh. 2.5 - Prob. 107ECh. 2.5 - Prob. 108ECh. 2.5 - Prob. 109ECh. 2.5 - Prob. 110ECh. 2.5 - Prob. 112ECh. 2.5 - Prob. 113ECh. 2.5 - Prob. 114ECh. 2.6 - Prob. 115UYKCh. 2.6 - Prob. 116UYKCh. 2.6 - Prob. 117UYKCh. 2.6 - Prob. 118UYKCh. 2.6 - Prob. 119UYKCh. 2.6 - Prob. 120UYKCh. 2.6 - Prob. 121ECh. 2.6 - Prob. 122ECh. 2.6 - Prob. 123ECh. 2.6 - Prob. 124ECh. 2.6 - Prob. 125ECh. 2.6 - Prob. 126ECh. 2.6 - Prob. 127ECh. 2.6 - Prob. 128ECh. 2.6 - Prob. 129ECh. 2.6 - Prob. 130ECh. 2.6 - Prob. 131ECh. 2.6 - Prob. 132ECh. 2.7 - Prob. 133ECh. 2.7 - Prob. 134ECh. 2.7 - Prob. 135ECh. 2.7 - Prob. 136ECh. 2.7 - Prob. 137ECh. 2.7 - Prob. 138ECh. 2.7 - Prob. 139ECh. 2.7 - Prob. 140ECh. 2.7 - Prob. 141ECh. 2.7 - Prob. 142ECh. 2.7 - Prob. 143ECh. 2.7 - Prob. 144ECh. 2.7 - Prob. 145ECh. 2 - Prob. 146ECh. 2 - Prob. 147ECh. 2 - Prob. 148ECh. 2 - Prob. 149ECh. 2 - Prob. 150ECh. 2 - Prob. 151ECh. 2 - Prob. 152ECh. 2 - Prob. 153ECh. 2 - Prob. 154ECh. 2 - Prob. 155ECh. 2 - Prob. 156ECh. 2 - Prob. 157ECh. 2 - Prob. 158ECh. 2 - Prob. 159ECh. 2 - Prob. 160ECh. 2 - Prob. 161ECh. 2 - Prob. 162ECh. 2 - Prob. 163ECh. 2 - Prob. 164ECh. 2 - Prob. 165ECh. 2 - Prob. 166ECh. 2 - Prob. 167ECh. 2 - Prob. 168ECh. 2 - Prob. 169ECh. 2 - Prob. 170ECh. 2 - Prob. 171ECh. 2 - Prob. 172ECh. 2 - Prob. 173ECh. 2 - Prob. 174ECh. 2 - Prob. 175ECh. 2 - Prob. 176ECh. 2 - Prob. 177ECh. 2 - Prob. 178E
Knowledge Booster
Background pattern image
Statistics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
Text book image
Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning
Text book image
Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning
Text book image
Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
Text book image
The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman
Text book image
Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman
The Shape of Data: Distributions: Crash Course Statistics #7; Author: CrashCourse;https://www.youtube.com/watch?v=bPFNxD3Yg6U;License: Standard YouTube License, CC-BY
Shape, Center, and Spread - Module 20.2 (Part 1); Author: Mrmathblog;https://www.youtube.com/watch?v=COaid7O_Gag;License: Standard YouTube License, CC-BY
Shape, Center and Spread; Author: Emily Murdock;https://www.youtube.com/watch?v=_YyW0DSCzpM;License: Standard Youtube License