Šuppose IQ scores were obtained from randomly selected siblings. For 20 such pairs of people, the linear correlation coefficient is 0.877 and the equation of the regression line is y = 20.45 +0.81x, where x represents the IQ score of the older child. Also, the 20 x values have a mean of 105.5 and the 20 y values have a mean of 105.75. What is the best predicted IQ of the younger child, given that the older child has an IQ of 103? Use a significance level of 0.05. E Click the icon to view the critical values of the Pearson correlation coefficient r. The best predicted IQ of the younger child is (Round to two decimal places as needed.)

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the table for critical value is given in image capture2.png

Suppose IQ scores were obtained from randomly selected siblings. For 20 such pairs of people, the linear correlation coefficient is 0.877 and the equation of the regression line is y = 20.45 + 0.81x, where x represents the IQ score of the older child. Also,
the 20 x values have a mean of 105.5 and the 20 y values have a mean of 105.75. What is the best predicted IQ of the younger child, given that the older child has an IQ of 103? Use a significance level of 0.05.
Click the icon to view the critical values of the Pearson correlation coefficient r.
The best predicted IQ of the younger child is
(Round to two decimal places as needed.)
Transcribed Image Text:Suppose IQ scores were obtained from randomly selected siblings. For 20 such pairs of people, the linear correlation coefficient is 0.877 and the equation of the regression line is y = 20.45 + 0.81x, where x represents the IQ score of the older child. Also, the 20 x values have a mean of 105.5 and the 20 y values have a mean of 105.75. What is the best predicted IQ of the younger child, given that the older child has an IQ of 103? Use a significance level of 0.05. Click the icon to view the critical values of the Pearson correlation coefficient r. The best predicted IQ of the younger child is (Round to two decimal places as needed.)
NOTE: To test H,: p=0
against H,: p#0, reject
H, if the absolute value
of r is greater than the
critical value in the
table.
Critical Values of the Pearson Correlation Coefficient r
(=0.05
x = 0.01
4
0.950
0.990
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
0.590
19
0.456
0.575
20
0.444
0.561
25
0.396
0.505
30
0.361
0.463
35
0.335
0.430
40
0.312
0.402
45
0.294
0.378
50
0.279
0.361
60
0.254
0.330
70
0.236
0.305
80
0.220
0.286
90
0.207
0.269
100
0.196
0.256
a = 0.05
a = 0.01
Transcribed Image Text:NOTE: To test H,: p=0 against H,: p#0, reject H, if the absolute value of r is greater than the critical value in the table. Critical Values of the Pearson Correlation Coefficient r (=0.05 x = 0.01 4 0.950 0.990 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 0.590 19 0.456 0.575 20 0.444 0.561 25 0.396 0.505 30 0.361 0.463 35 0.335 0.430 40 0.312 0.402 45 0.294 0.378 50 0.279 0.361 60 0.254 0.330 70 0.236 0.305 80 0.220 0.286 90 0.207 0.269 100 0.196 0.256 a = 0.05 a = 0.01
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