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To find: The joint distribution, marginal distribution, and conditional distribution.
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:
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 |
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Private |
Public |
|
Marginal distribution |
||
The marginal distribution of Physical education course is shown below:
Physical education course |
Marginal distribution |
Yes |
|
No |
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:
The conditional distribution for Physical education course by each Educational institution is shown below:
Physical education course |
Private |
Public |
Yes |
||
No |
||
Total |
To explain: The conditional distribution to explain the result of the analysis.
Answer to Problem 18E
Solution: The Conditional distribution of ‘Physical education course by educational institutions’ is more preferable.
Explanation of Solution
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Chapter 9 Solutions
Introduction to the Practice of Statistics
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