Suppose IQ scores were obtained from randomly selected siblings.For 20such pairs
ID: 3219096 • Letter: S
Question
Suppose IQ scores were obtained from randomly selected siblings.For 20such pairs of people, the linear correlation coefficient is 0.915 and the equation of the regression line is
ModifyingAbove y=10.37+0.91x,
where x represents the IQ score of the older child. Also, the 20 x values have a mean of 104.18 and the 20 y values have a mean of105.55.
What is the best predicted IQ of the younger child,given that the older child has an IQ of 92?
Use a significance level of 0.05.
The best predicted IQ of the younger child is?
Critical Values of the Pearson Correlation Coefficient r
H0:=0 against
H1:0,rejectH0
n
=0.05
=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
n
=0.05
=0.01
Critical Values of the Pearson Correlation Coefficient r
NOTE: To testH0:=0 against
H1:0,rejectH0
if the absolute value of r is greater than the critical value in the table.n
=0.05
=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
n
=0.05
=0.01
Explanation / Answer
For n = 20 and significance level of 0.05,
Critical r value = 0.444
According to question
Calculated r value = 0.915
Since this is greater than the critical value, a linear relationship exists between the two variable.
Hence,
For x = 92,
y = 10.37 + 0.91 (92)
y = 94.09
So,
The best predicted IQ of the younger child, given that the older child has an IQ of 92 is 94.09.
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