Question

In: Statistics and Probability

IQ tests are sometimes used to assess children’s cognitive abilities. However, typical IQ tests draw on...

IQ tests are sometimes used to assess children’s cognitive abilities. However, typical IQ tests draw on reading skills, which
may translate into lower scores for dyslexic children. Nonverbal IQ tests should circumvent this issue, allowing us to ask
whether there is a relationship between reading skills and cognitive abilities in dyslexic children. The table below gives the reading
skill scores (on a standardized scale) and the nonverbal IQ scores (also on a standardized scale) of 22 dyslexic children aged
7 to 10 years. Are the reading skill scores and nonverbal IQ scores significantly correlated in young dyslexic children?
Child # Reading skill score Nonverbal IQ score
1 84 93
2 81 103
3 85 102
4 82 99
5 87 98
6 85 91
7 89 123
8 86 95
9 85 125
10 83 75
11 76 106
12 76 77
13 75 98
14 78 108
15 86 96
16 73 86
17 79 117
18 95 119
19 85 91
20 93 103
21 84 84
22 88 93
Ho:
Ha:
test-statistic:
df:
Exact P value for the test-statistic
Conclusion relative to the hypothesis:
ts= ,df= ,P=

Solutions

Expert Solution

: correlation coefficient between Reading skill score and Non verbal IQ score in young dyslexic children

Null hypothesis : Ho : = 0

Alternate Hypothesis : Ha : 0

Formula for sample correlation coefficient :r

x: Reading skill score

y: Non verbal IQ score

Child # x:Reading skill score y:Nonverbal IQ score xy x2 y2
1 84 93 7812 7056 8649
2 81 103 8343 6561 10609
3 85 102 8670 7225 10404
4 82 99 8118 6724 9801
5 87 98 8526 7569 9604
6 85 91 7735 7225 8281
7 89 123 10947 7921 15129
8 86 95 8170 7396 9025
9 85 125 10625 7225 15625
10 83 75 6225 6889 5625
11 76 106 8056 5776 11236
12 76 77 5852 5776 5929
13 75 98 7350 5625 9604
14 78 108 8424 6084 11664
15 86 96 8256 7396 9216
16 73 86 6278 5329 7396
17 79 117 9243 6241 13689
18 95 119 11305 9025 14161
19 85 91 7735 7225 8281
20 93 103 9579 8649 10609
21 84 84 7056 7056 7056
22 88 93 8184 7744 8649
Total =1835 =2182 =182489 =153717 =220242

test statistic :

test statistic = 1.448971086

degrees of freedom :df = n-2 =20

df: 20

For two tailed test

For 20 degrees of freedom , P(t>1.448971086) = 0.081422231

p-value = 2x P(t > tstat) = 2x P(t>1.448971086) =2 x 0.081422231 = 0.162844461

p-value = 0.162844461

Exact P value for the test-statistic = 0.162844461

As p-value > level of significance : :0.05 ; Fail to reject the null hypothesis.

Conclusion relative to the hypothesis: Fail to reject the null hypothesis.

There is not enough evidence to conclude that the the reading skill scores and nonverbal IQ scores are significantly correlated in young dyslexic children

ts=1.448971086

df=20

p=0.162844461


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