Question

Kuya conducted a study to investigate if children improve in their Verbal IQ within a period of about seven years, when they were at age 6 and when they turned 13. The test scores range from 1 to 30.

VERBAL IQ
Age 6	Age 13
20	17
22	21
10	20
17	21
21	18
17	23
13	16
26	18
14	16
17	21
14	20
20	21
14	16
21	21
10	16
22	18
26	22
17	23
16	21
20	15
14	21
21	19
22	22
12	18
20	15
14	20
20	18
20	21
20	21
10	22
17	18
10	22
16	21
11	15
16	15
13	19

The appropriate test for this problem is:

t test for one sample

t test for dependent samples

t test for independent samples

The obtained statistic is:

t = - 7.2

t = 7.2

t = - 2.7

t = 2.7

The associated p value is:

.10

.011

.001

.0011

Decision is:

reject the null

retain the null

Conclusion is:

verbal IQ scores increased significantly

verbal IQ scores decreased significantly

verbal IQ scores remain about the same

no conclusion can be drawn

Answer 1

Solution:

Here we will use t test for dependent samples. because both samples are same only age difference is there. so both samples are dependent on each other and we will use t test for dependent samples.

Now we will calculate Difference b/w each samples

Age6	Age13	D
20	17	-3
22	21	-1
10	20	10
17	21	4
21	18	-3
17	23	6
13	16	3
26	18	-8
14	16	2
17	21	4
14	20	6
20	21	1
14	16	2
21	21	0
10	16	6
22	18	-4
26	22	-4
17	23	6
16	21	5
20	15	-5
14	21	7
21	19	-2
22	22	0
12	18	6
20	15	-5
14	20	6
20	18	-2
20	21	1
20	21	1
10	22	12
17	18	1
10	22	12
16	21	5
11	15	4
16	15	-1
13	19	6

Dbar = 2.166667

SD = 4.819603

n= 37

test statistic = Dbar/SD/sqrt(n)

test statistic = 2.166667/4.819603/sqrt(37)

test statistic = 2.734 or 2.7

so test statistic answer is D. i.e. 2.7

associated values is

here degree of freedom = 37-1 =36

and it is a two tailed test

so p-value is 0.01

and at alpha = 0.05 or 95% confidence interval

we will reject the null hypothesis so its answer is A.

If we are rejecting the null hypothesis which means that verbal IQ scores is not remain about the same. so its answer is D. i.e. no conclusion can be drawn.