Question

It appears that sons of fathers who display low self-esteem tend to develop low self-esteem as well. Kuya conducted a study to test this hypothesis, since he is pretty sure that there must be a difference between the two groups, with sons having higher self-esteem than their fathers. He measured the self-esteem of the fathers and their sons using the Fearful Insecure Neurotic Emotional (FINE) test. The higher the score, the lower is the self-esteem. Is there a significant difference?

SON	FATHER
32	24
24	27
32	31
30	30
29	34
31	22
22	18
22	24
24	31
28	31
28	36
33	29
29	35
24	28
30	35
23	27
32	38
28	35
23	30
32	36
28	38
31	21
25	39
33	39
26	32
23	36
23	13
22	27
32	30
32	39
30	37
25	32
32	33
33	37
28	34
23	20
23	25
26	27
33	21
28	20
33	36

The appropriate test for this problem is:

1. t test for one sample
2. t test for dependent samples
3. t test for independent samples
4. one-way ANOVA
5. repeated measurements ANOVA

The obtained statistic value is:

1. 29.049
2. 40
3. -2.24
4. -2.29

The associated p value is:

1. .05
2. < .05
3. < .01
4. < .001

Decision is:

1. reject the null
2. retain the null

Conclusion is:

1. fathers have lower self-esteem than their sons
2. sons have lower self-esteem than their fathers
3. fathers and sons have about equal self-esteem scores
4. no conclusion can be drawn

Answer 1

H0: mu(d) = 0
Ha: mu(d) not equals to 0

from the given data,
dbar = -2.2439
s(dbar) = 6.2681

t test for dependent samples

Test statistic,
t = -2.2439/(6.2681/sqrt(41))
t = -2.2922

option D

p-value < 0.05

Reject H0

fathers have lower self-esteem than their sons