Two Independent Samples t-test You want to find out whether a particular form of
ID: 3225157 • Letter: T
Question
Two Independent Samples t-test You want to find out whether a particular form of cognitive behavioral therapy decreases depressive symptoms in patients a symptom score that from 0 to 50 (with 50 the most You do study in which randomly sampled patients are assigned to a group and five randomly sampled patients are assigned to control group, which receives no treatment. We are assuming that the two populations have the same standard deviation, Alpha is set to .05 1. What is your null and alternative hypothesis (n words AND symbols? Remember: You need to state these hypotheses in terms of population means (5pt) 2. The mean for the control group sample is 35 and the mean for the treatment group sample is 25. Find the pooled estimate of the population standard deviation using the table and formulas below (15pt) Group Symptom Group mean Deviation from mean Squared deviation Score mean Score Control Control Control Control Control Treatment Treatment Treatment Treatment Sum of squared deviationsExplanation / Answer
Q-1
Null hypothesis H0: µtreatment = µcontrol versus the alternative Ha: µtreatment < µcontrol
Null hypothesis H0: There is not difference in depression score of treatment and control.
Alternative hypothesis Ha: The depression score of treatment is lower than control.
Q-2
Group
Symptom Score
Group Mean
Deviation from Mean=Score-Mean
Squared deviations =(score-Mean)^2
Control
35
35
0
0
Control
37
35
2
4
Control
26
35
-9
81
Control
39
35
4
16
Control
38
35
3
9
Treatment
32
25
7
49
Treatment
28
25
3
9
Treatment
22
25
-3
9
Treatment
19
25
-6
36
Treatment
24
25
-1
1
Sum of Sqaured Deviations=
214
SDpooled = sqrt(214/(5+5-2)) =5.17
SEdifference = 5.17*sqrt(1/5+1/5) =3.27
Q-3
Test statistic ttest= (35-25)/3.27 =3.06
Group
Symptom Score
Group Mean
Deviation from Mean=Score-Mean
Squared deviations =(score-Mean)^2
Control
35
35
0
0
Control
37
35
2
4
Control
26
35
-9
81
Control
39
35
4
16
Control
38
35
3
9
Treatment
32
25
7
49
Treatment
28
25
3
9
Treatment
22
25
-3
9
Treatment
19
25
-6
36
Treatment
24
25
-1
1
Sum of Sqaured Deviations=
214
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