Question
At the .05 significance level, does the data below show significant correlation? x y 5 21.1...
At the .05 significance level, does the data below show
significant correlation?
| x | y |
|---|---|
| 5 | 21.1 |
| 6 | 25.22 |
| 7 | 29.34 |
| 8 | 16.26 |
| 9 | 15.18 |
| 10 | 20.9 |
- Yes, significant correlation
- No
Homework Answers
Answer #1
Solution:
| X | Y | XY | X^2 | Y^2 |
| 5 | 21.1 | 105.5 | 25 | 445.21 |
| 6 | 25.22 | 151.32 | 36 | 636.0484 |
| 7 | 29.34 | 205.38 | 49 | 860.8356 |
| 8 | 16.26 | 130.08 | 64 | 264.3876 |
| 9 | 15.18 | 136.62 | 81 | 230.4324 |
| 10 | 20.9 | 209 | 100 | 436.81 |
| n | 6 |
| sum(XY) | 937.90 |
| sum(X) | 45.00 |
| sum(Y) | 128.00 |
| sum(X^2) | 355.00 |
| sum(Y^2) | 2873.72 |
| Numerator | -132.60 |
| Denominator | 300.21 |
| r | -0.4417 |
| r square | 0.1951 |
| Xbar(mean) | 7.5000 |
| Ybar(mean) | 21.3333 |
| SD(X) | 1.7078 |
| SD(Y) | 4.8829 |
| b | -1.2629 |
| a | 30.8048 |
Therefore, the correlation coefficient r = -0.4417
df = n - 2 = 4
= 0.05
= 0.025
The critical value is = 0.811
Therefore, r = -0.4417 < 0.811, there is fail to reject the null hypothesis.
No, there is not significant correlation.
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