Suppose IQ scores were obtained from randomly selected couples. For 20 such pair
ID: 3125746 • Letter: S
Question
Suppose IQ scores were obtained from randomly selected couples. For 20 such pairs of people, the linear correlation coefficient is 0.9140.914 and the equation of the regression line is ModifyingAbove y with caret equals 9.18 plus 0.91 xy=9.18+0.91x , where x represents the IQ score of the wife. Also, the 20 x values have a mean of 96.62 and the 2020 y values have a mean of 96.65. What is the best predicted IQ of the husband given that the wife has an IQ of 98 ? Use a significance level of 0.05.
Critical Values of the Pearson Correlation Coefficient r
H0:
rhoequals=0
H1:
rhonot equals0,
H0
n
alphaequals=0.05
alphaequals=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
alphaequals=0.05
alphaequals=0.01
PrintDone
Critical Values of the Pearson Correlation Coefficient r
NOTE: To testH0:
rhoequals=0
againstH1:
rhonot equals0,
rejectH0
if the absolute value of r is greater than the critical value in the table.n
alphaequals=0.05
alphaequals=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
alphaequals=0.05
alphaequals=0.01
Explanation / Answer
The question really is
"What is the best predicted IQ of the husband given that the wife has an IQ of 98 ?"
Hence, as
y^ = 9.18 + 0.91x
Then as x = 98 here,
y^ = 9.18 + 0.91*98 = 98.36 [ANSWER]
************************
The other givens would not matter, at least for this question. Thanks!
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