Question
In: Statistics and Probability
You wish to determine if there is a linear correlation between the two variables at a...
You wish to determine if there is a linear correlation between the two variables at a significance level of α=0.10. You have the following bivariate data set.
| x | y |
|---|---|
| 30.5 | 114.8 |
| 40.9 | 130.6 |
| 25.9 | 19.8 |
| 25.1 | 23.9 |
| 27.9 | 96.4 |
| 40.8 | 91.6 |
| 32.4 | 41.1 |
| 27.6 | 34 |
| 38.3 | 145.8 |
| 32.8 | 138.8 |
| 32.5 | 95.5 |
| 37.4 | 120.4 |
| 22 | 84.6 |
| 41 | 65.6 |
| 30.8 | 27.4 |
| 21.8 | 102 |
| 33 | 66.4 |
| 31.9 | 59.8 |
| 27.8 | 41.4 |
| 30.1 | 85.8 |
| 26.2 | 71.7 |
| 28.5 | 35.1 |
| 26.9 | 67.6 |
1. What is the correlation coefficient for this
data set?
r =
2. To find the p-value for a correlation coefficient, you need to convert to a t-score:
t=√r2(n−2)/(1−r2)
This t-score is from a t-distribution with
n–2 degrees of freedom.
What is the p-value for this correlation coefficient?
p-value =
3. Your final conclusion is that...
A) There is sufficient sample evidence to support the claim that there is a statistically significant correlation between the two variables.
B) There is insufficient sample evidence to support the claim the there is a correlation between the two variables.
Solutions
Expert Solution
| X | Y | X * Y |
 |
 |
|
| 30.5 | 114.8 | 3501.4 | 930.25 | 13179.04 | |
| 40.9 | 130.6 | 5341.54 | 1672.81 | 17056.36 | |
| 25.9 | 19.8 | 512.82 | 670.81 | 392.04 | |
| 25.1 | 23.9 | 599.89 | 630.01 | 571.21 | |
| 27.9 | 96.4 | 2689.56 | 778.41 | 9292.96 | |
| 40.8 | 91.6 | 3737.28 | 1664.64 | 8390.56 | |
| 32.4 | 41.1 | 1331.64 | 1049.76 | 1689.21 | |
| 27.6 | 34 | 938.4 | 761.76 | 1156 | |
| 38.3 | 145.8 | 5584.14 | 1466.89 | 21257.64 | |
| 32.8 | 138.8 | 4552.64 | 1075.84 | 19265.44 | |
| 32.5 | 95.5 | 3103.75 | 1056.25 | 9120.25 | |
| 37.4 | 120.4 | 4502.96 | 1398.76 | 14496.16 | |
| 22 | 84.6 | 1861.2 | 484 | 7157.16 | |
| 41 | 65.6 | 2689.6 | 1681 | 4303.36 | |
| 30.8 | 27.4 | 843.92 | 948.64 | 750.76 | |
| 21.8 | 102 | 2223.6 | 475.24 | 10404 | |
| 33 | 66.4 | 2191.2 | 1089 | 4408.96 | |
| 31.9 | 59.8 | 1907.62 | 1017.61 | 3576.04 | |
| 27.8 | 41.4 | 1150.92 | 772.84 | 1713.96 | |
| 30.1 | 85.8 | 2582.58 | 906.01 | 7361.64 | |
| 26.2 | 71.7 | 1878.54 | 686.44 | 5140.89 | |
| 28.5 | 35.1 | 1000.35 | 812.25 | 1232.01 | |
| 26.9 | 67.6 | 1818.44 | 723.61 | 4569.76 | |
| Total | 712.1 | 1760.1 | 56543.99 | 22752.83 | 166485.41 |
r = 0.4328
To Test :-
H0 :- 
H1 :- 
Test Statistic :-
t = 2.2
Test Criteria :-
Reject null hypothesis if 
Result :- Reject null hypothesis
Decision based on P value
P - value = P ( t > 2.2 ) = 0.0391
Reject null hypothesis if P value < 
level of significance
P - value = 0.0391 < 0.1 ,hence we reject null hypothesis
Conclusion :- We reject H0
A) There is sufficient sample evidence to support the claim that there is a statistically significant correlation between the two variables.
orchestra answered 2 years agoRelated Solutions
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To find the p-value for a correlation coefficient, you need to
convert to a t-score:
t=√r2(n−2)1−r2...
You wish to determine if there is a linear correlation between the two variables at a...
You wish to determine if there is a linear correlation between
the two variables at a significance level of α=0.005α=0.005. You
have the following bivariate data set.
x
y
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65.2
27.9
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