Two Independent Samples t-test You want to find out whether a particular form of
ID: 3225163 • 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. You use a symptom score that ranges from 0 to 50 (with 50 being the most severe depression). You do a small study in which five randomly sampled patients are assigned to a treatment 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 altemative hypothesis (in words AND symbols)? (Remember: You need to state these hypotheses in tems 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-mean) 35 Control Control 37 Control 26 39 Control 38 Control Treatment 32 28 Treatment Treatment 19 Treatment 24 Treatment Sum of squared deviationsExplanation / Answer
Q-1
Null hypothesis H0: µ1 = µ2 is to be tested against the alternative Ha: µ1 < µ2 where µ1 = µ2 are the true means of treatment and control
Null hypothesis H0: There is not difference in mean depression score of treatment and control.
Alternative hypothesis Ha: The mean 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
SD(pooled)hat = sqrt(sum of squared dviations/(n1+n2-2)=sqrt(214/(5+5-2)) =5.172
SE(difference)hat= SD(pooled)hat *sqrt(1/n1+1/n2) =sqrt( 5.172*sqrt(1/5+1/5) =3.271
Q-3
Test statistic t= (35-25)/3.271=3.0572
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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