EBK INTRODUCTION TO THE PRACTICE OF STA
EBK INTRODUCTION TO THE PRACTICE OF STA
9th Edition
ISBN: 8220103674638
Author: Moore
Publisher: YUZU
bartleby

Videos

Question
Book Icon
Chapter 9.1, Problem 18E
To determine

To find: The joint distribution, marginal distribution, and conditional distribution.

Expert Solution
Check Mark

Answer to Problem 18E

Solution: In the study, 16.95% private institutions required physical education course and 28.53% of public institutions required the same. 46.61% of private institutions do not require physical education course and 7.90% of public institutions do not require the same. Among those who required the physical education course, 37.27% are private and 62.73% are public institutions, and among those who do not require physical education course, 85.49% are private and 14.51% are public.

Explanation of Solution

Calculation:

In the study, there are 354 higher institutions in which 225 are private institutions and 129 are public. Out of 225 private institutions, 60 require a physical education course. Out of 129 public institutions, 101 require a physical education course. In the study, Joint distribution is computed by dividing the cell element by the total observation. The obtained joint distribution is shown below:

Educational institutionsPhysical education coursePrivatePublicTotalYes(60354×100=16.95%)(101354×100=28.53%)(161354×100=45.48%)No(165354×100=46.61%)(28354×100=7.90%)(193354×100=54.51%)Total(225354×100=63.66%)(129354×100=36.44%)(354354×100=100%)

Now, the marginal distribution is computed by dividing the row or column totals by the overall total. Marginal distributions provide information about the individual variables but not about the relationship between two variables. Thus, the marginal distribution of Educational institutions is shown below:

Educational institutions

Private

Public

Marginal distribution

(225354×100%=63.56)

(129354×100%=36.44%)

The marginal distribution of Physical education course is shown below:

Physical education course

Marginal distribution

Yes

(161354×100%=45.48%)

No

(193354×100%=54.52%)

Conditional distribution is obtained by dividing the row or column elements by the sum of the observations in the corresponding row or column. The conditional distribution of Educational institutions by Physical education course is shown below:

Educational institutionsPhysical education coursePrivatePublicTotalYes(60161×100=37.27%)(101161×100=62.73%)(161161×100=100%)No(165193×100=85.49%)(28193×100=14.51%)(193193×100=100%)

The conditional distribution for Physical education course by each Educational institution is shown below:

Physical education course

Private

Public

Yes

(60225×100=26.66%)

(101129×100=78.29%)

No

(165225×100=73.33%)

(28129×100=21.71%)

Total

(225225×100=100%)

(129129×100=100%)

To determine

To explain: The conditional distribution to explain the result of the analysis.

Expert Solution
Check Mark

Answer to Problem 18E

Solution: The Conditional distribution of ‘Physical education course by educational institutions’ is more preferable.

Explanation of Solution

The use of physical education course is more informative. A lot many public institutions require physical education course than the private institutions. From the above conditional distribution, a higher percentage of public institutions requires physical education course than the private institutions.

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?
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
F- Test or F- statistic (F- Test of Equality of Variance); Author: Prof. Arvind Kumar Sing;https://www.youtube.com/watch?v=PdUt7InTyc8;License: Standard Youtube License
Statistics 101: F-ratio Test for Two Equal Variances; Author: Brandon Foltz;https://www.youtube.com/watch?v=UWQO4gX7-lE;License: Standard YouTube License, CC-BY
Hypothesis Testing and Confidence Intervals (FRM Part 1 – Book 2 – Chapter 5); Author: Analystprep;https://www.youtube.com/watch?v=vth3yZIUlGQ;License: Standard YouTube License, CC-BY
Understanding the Levene's Test for Equality of Variances in SPSS; Author: Dr. Todd Grande;https://www.youtube.com/watch?v=udJr8V2P8Xo;License: Standard Youtube License