Suppose IQ scores were obtained from randomly selected siblings. For 20 such pai
ID: 3158696 • Letter: S
Question
Suppose IQ scores were obtained from randomly selected siblings. For 20 such pairs of people, the linear correlation coefficient is 0.915 and the equation of the regression line is y=1.78+0.99x, where x represents the IQ score of the older child. Also, the 20 x values have a mean of 97.32 and the 20 y values have a mean of 98.1. What is the best predicted IQ of the younger child, given that the older child has an IQ of 102? Use a significance level of 0.05.
Critical Values of the Pearson Correlation Coefficient r
n
equals=0.05
equals=0.01
4
0.950
0.990
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
0.590
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
Critical Values of the Pearson Correlation Coefficient r
n
equals=0.05
equals=0.01
4
0.950
0.990
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
0.590
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
Explanation / Answer
The IQ of the younger child can be predicted by the regression model.
y = 1.78+0.99*102 = 102.76
Thus the younger child should have an IQ of 102.76
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