a.
To Calculate:
The
Answer to Problem 19E
Solution:
The
Explanation of Solution
Given:
Mothers’ Birth Weights and Babies’ Birth Weights | |||||||||||||||||
Mother | lb | 6 | 6 | 7 | 8 | 7 | 7 | 7 | 6 | 9 | 6 | 9 | 8 | 6 | 5 | 6 | 5 |
oz | 6 | 2 | 9 | 10 | 6 | 15 | 7 | 5 | 3 | 10 | 3 | 9 | 1 | 0 | 1 | 0 | |
Baby | lb | 5 | 6 | 7 | 7 | 10 | 5 | 9 | 5 | 8 | 7 | 9 | 8 | 5 | 7 | 7 | 8 |
oz | 11 | 14 | 10 | 2 | 0 | 13 | 0 | 9 | 13 | 11 | 10 | 6 | 8 | 15 | 2 | 5 |
Since one pound is equal to 16 ounce converting pounds (lb) to ounce (Oz) we have,
Mother | 102 | 98 | 121 | 138 | 118 | 127 | 119 | 101 | 147 | |||
Baby | 91 | 110 | 122 | 114 | 160 | 93 | 144 | 89 | 141 | |||
Mother | 106 | 147 | 137 | 97 | 80 | 97 | 80 | |||||
Baby | 123 | 150 | 134 | 88 | 127 | 114 | 133 | |||||
Formula:
The Pearson correlation coefficient for paired data from a sample is given by:
Where n is the number of data pairs of the sample,
Calculation:
Using the above table we have,
Mother weight (lb)xi | Babies weight (lb)yi | (xi)(yi) | xi 2 | yi 2 |
102 | 91 | 9282 | 10404 | 8281 |
98 | 110 | 10780 | 9604 | 12100 |
121 | 122 | 14762 | 14641 | 14884 |
138 | 114 | 15732 | 19044 | 12996 |
118 | 160 | 18880 | 13924 | 25600 |
127 | 93 | 11811 | 16129 | 8649 |
119 | 144 | 17136 | 14161 | 20736 |
101 | 89 | 8989 | 10201 | 7921 |
147 | 141 | 20727 | 21609 | 19881 |
106 | 123 | 13038 | 11236 | 15129 |
147 | 154 | 22638 | 21609 | 23716 |
137 | 134 | 18358 | 18769 | 17956 |
97 | 88 | 8536 | 9409 | 7744 |
80 | 127 | 10160 | 6400 | 16129 |
97 | 114 | 11058 | 9409 | 12996 |
80 | 133 | 10640 | 6400 | 17689 |
Here n=16, Substituting the total values in (1),
Thus, the correlation coefficient is,
Whether the correlation coefficient is statistically significant at the 0.05 level of significance.
Answer to Problem 19E
Solution:
The correlation coefficient is not statistically significant at the level of significance
Explanation of Solution
Procedure:
The correlation coefficient
Where
On other hand,
A sample correlation coefficient,
Given:
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 not statistically significant at the level of significance
(c)
To Find:
The coefficient of determination,
Answer to Problem 19E
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 19E
Solution:
The variation in the babies’ birth weights can be associated with the variation in birth weights of the mothers by
Explanation of Solution
The correlation coefficient for the babies’ birth weights with the birth weights of the mothers is
The coefficient of determination,
Coefficient of determination is,
Interpretation:
Thus, approximately
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