Use the given data set to complete parts​ (a) through​ (c) below.​ (Use α=​0.05.) a. Find the linear correlation​ coefficient, r, then determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables.   The linear correlation coefficient is r= ​(Round to three decimal places as​ needed.)

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Use the given data set to complete parts​ (a) through​ (c) below.​ (Use α=​0.05.)

a. Find the linear correlation​ coefficient, r, then determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables.

 
The linear correlation coefficient is
r=
​(Round to three decimal places as​ needed.)
X
y
10
7.46
8
6.78
13
12.74
9
7.11
11
7.81
14
8.84
6
6.08
4
5.39
12
8.14
7
6.41
5
5.73
Transcribed Image Text:X y 10 7.46 8 6.78 13 12.74 9 7.11 11 7.81 14 8.84 6 6.08 4 5.39 12 8.14 7 6.41 5 5.73
4
5
6
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8
9
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11
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25
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100
α = .05
.950
.878
.811
.754
.707
.666
.632
.602
.576
.553
.532
.514
.497
.482
.468
.456
.444
.396
.361
.335
.312
.294
.279
254
.236
.220
.207
.196
α = .01
.990
.959
.917
.875
.834
.798
.765
.735
.708
.684
.661
.641
.623
.606
.590
.575
.561
.505
.463
.430
.402
.378
.361
.330
.305
.286
.269
.256
NOTE: To test Ho: P = 0 against H₁: p = 0,
reject Ho if the absolute value of r is
greater than the critical value in the table.
Transcribed Image Text:4 5 6 7 8 9 10 11 23456789 12 13 14 15 16 17 18 19 20 25 30 35 40 45 50 60 70 80 90 100 α = .05 .950 .878 .811 .754 .707 .666 .632 .602 .576 .553 .532 .514 .497 .482 .468 .456 .444 .396 .361 .335 .312 .294 .279 254 .236 .220 .207 .196 α = .01 .990 .959 .917 .875 .834 .798 .765 .735 .708 .684 .661 .641 .623 .606 .590 .575 .561 .505 .463 .430 .402 .378 .361 .330 .305 .286 .269 .256 NOTE: To test Ho: P = 0 against H₁: p = 0, reject Ho if the absolute value of r is greater than the critical value in the table.
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