(a)
To Calculate:
The
Answer to Problem 18E
Solution:
The
Explanation of Solution
Given:
Number of Absences and class Average | ||||||||||||||||
Absences | 2 | 2 | 3 | 10 | 3 | 7 | 9 | 1 | 12 | 9 | 1 | 1 | 13 | 1 | 10 | 3 |
Class Average | 86 | 83 | 81 | 53 | 92 | 71 | 68 | 79 | 53 | 78 | 77 | 85 | 62 | 97 | 54 | 79 |
Formula used:
Pearson Correlation Coefficient:
The Pearson Correlation Coefficient for paired data from a sample:
Where
While
Calculation:
Let
Here,
2 | 86 | 172 | 4 | 7396 |
2 | 83 | 166 | 4 | 6889 |
3 | 81 | 243 | 9 | 6561 |
10 | 53 | 530 | 100 | 2809 |
3 | 92 | 276 | 9 | 8464 |
7 | 71 | 497 | 49 | 5041 |
9 | 68 | 612 | 81 | 4624 |
1 | 79 | 79 | 1 | 6241 |
12 | 53 | 636 | 144 | 2809 |
9 | 78 | 702 | 81 | 6084 |
1 | 77 | 77 | 1 | 5929 |
1 | 85 | 85 | 1 | 7225 |
13 | 62 | 806 | 169 | 3844 |
1 | 97 | 97 | 1 | 9409 |
10 | 54 | 540 | 100 | 2916 |
3 | 79 | 237 | 9 | 6241 |
To find Pearson Correlation Coefficient
Therefore, the correlation coefficient of
(b)
The type of distribution to use for the test statistics and state the level of significance.
Answer to Problem 18E
Solution:
The correlation coefficient is statistically significant at the level of significance
Explanation of Solution
Procedure:
The correlation coefficient
Where
On other hand,
A sample correlation coefficient,
Given:
Correlation Coefficient is
To find the critical value
The critical value
Comparing this critical value to the absolute value of the correlation coefficient. We get the relation,
Thus,
Therefore the correlation coefficient is statistically significant at the level of significance
(c)
To Find:
The coefficient of determination,
Answer to Problem 18E
Solution:
The coefficient of determination
Explanation of Solution
Definition:
The coefficient of determination,
Calculation:
Correlation Coefficient is
Coefficient of determination is the square of the Correlation Coefficient.
Then,
Thus, the Coefficient of determination
(d)
To Interpret:
The Coefficient of determination
Answer to Problem 18E
Solution:
Explanation of Solution
The correlation coefficient for the relationship between the number of Absences a student had for the semester and their class average is
The coefficient of determination,
Coefficient of determination is,
Interpretation:
Thus, approximately
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Chapter 12 Solutions
Beginning Statistics, 2nd Edition
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