At the .05 significance level, does the data below show significant correlation?
At the .05 significance level, does the data below show significant correlation?
| x | y |
|---|---|
| 5 | 23.6 |
| 6 | 17.08 |
| 7 | 20.06 |
| 8 | 29.84 |
| 9 | 30.02 |
| 10 | 21.1 |
| 11 | 20.28 |
| 12 | 25.76 |
| 13 | 27.24 |
| 14 | 31.32 |
| 15 | 30.5 |
| 16 | 21.38 |
Yes, significant correlation
No
Homework Answers
| ΣX | ΣY | Σ(x-x̅)² | Σ(y-ȳ)² | Σ(x-x̅)(y-ȳ) | |
| total sum | 126.00 | 298.18 | 143.00 | 263.82 | 74.29 |
| mean | 10.50 | 24.85 | SSxx | SSyy | SSxy |
correlation coefficient , r = SSxy/√(SSx.SSy)
= 0.38248
n= 12
alpha,α = 0.05
correlation , r= 0.3825
t-test statistic = r*√(n-2)/√(1-r²) =
1.3090
DF=n-2 = 10
p-value = 0.2198
Decison: P value > α, So, Do not reject
Ho
answer: NO
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At the .05 significance level, does the data below show significant correlation?
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Critical Values for the Correlation
Coefficient
n
alpha = .05
alpha = .01
4
0.95
0.99
5
0.878
0.959
6
0.811
0.917
7
0.754
0.875
8
0.707
0.834
9
0.666
0.798
10
0.632
0.765
11
0.602
0.735
12
0.576
0.708
13
0.553
0.684
14
0.532
0.661
15
0.514
0.641
16
0.497
0.623
17
0.482
0.606
18
0.468
0.59
19
0.456
0.575
20
0.444
0.561
25
0.396
0.505
30
0.361
0.463
35
0.335
0.43
40
0.312
0.402
45
0.294
0.378
50...
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Critical Values for the Correlation
Coefficient
n
alpha = .05
alpha = .01
4
0.95
0.99
5
0.878
0.959
6
0.811
0.917
7
0.754
0.875
8
0.707
0.834
9
0.666
0.798
10
0.632
0.765
11
0.602
0.735
12
0.576
0.708
13
0.553
0.684
14
0.532
0.661
15
0.514
0.641
16
0.497
0.623
17
0.482
0.606
18
0.468
0.59
19
0.456
0.575
20
0.444
0.561
25
0.396
0.505
30
0.361
0.463
35
0.335
0.43
40
0.312
0.402
45
0.294
0.378
50...
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