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 1 year agoRelated Solutions
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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=0.01. You have the
following bivariate data set.
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y
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42.7
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34.5
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What is the correlation coefficient for this data set?
r =
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
13.6
126.6
33.5
42.2
17.6
78.5
39
32.7
33
61.5
47.1
25.1
41.4
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112.8
40.6
32.6
27.3
63.2
27.6
59.6
31.4
52.7
56.6
9.1
55
28.6
40.5
46.3
17.9
91.8
52.1
-6.6
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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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(report answer accurate to at least 3 decimal places)
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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=0.01. You have the
following bivariate data set.
x
y
75
22.4
50.4
41.3
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60.1
35
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59
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54.5
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75.8
19.2
49.4
46.4
42.5
59.4
29.7
59.3
65.2
27.9
56.6
31.2
38.6
48.3
50.7
32.9
60
35.1
61
35.6
59.2
32.7
94.4
11.8
42.3
47.5
71.1
19.3
65.9
42.2
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What is the...
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62.5
112.7
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103
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What is the critival value for this hypothesis test?
rc.v. =
What is the correlation coefficient for this data set?
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30.8
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104.9
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1. The linear correlation coefficient r measures of the linear relationship between two variables. (a) Distance...
1. The linear correlation coefficient r measures of the linear
relationship between two variables. (a) Distance (b) size (c)
strength (d) direction 2. 10 pairs of sample data were obtained
from a study which looked at household income and the number of
people in the household who smoked (cigarettes). The value of the
linear correlation coefficient r was computed and a result of -
0.989 was obtained. All of the following (below) are conclusions
that can be drawn from the...
1. The linear correlation coefficient r measures of the linear relationship between two variables. (a) Distance...
1. The linear correlation coefficient r measures of the linear
relationship between two variables. (a) Distance (b) size (c)
strength (d) direction 2. 10 pairs of sample data were obtained
from a study which looked at household income and the number of
people in the household who smoked (cigarettes). The value of the
linear correlation coefficient r was computed and a result of -
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