Assignment 2: Significance t-Test for a Single Sample

Tests of Significance
Name of Student
Institution Affiliation
Tests of Significance
Mock Study 1: t-Test for a Single Sample
Research hypothesis
Alternative hypothesis
Null Hypothesis
H0: Average number of activities of daily living obtained after therapy is significantly different from a mean number of activities of 17 (typical for depressed people).
Alternative Hypothesis
H1: Average number of activities of daily living obtained after therapy is not significantly different from a mean number of activities of 17 (typical for depressed people).
This study mock uses both .05 and .01 significance levels to test the hypotheses
The following data is uploaded onto IBM SPSS 24 for analysis:
CLIENT

AFTER THERAPY

A

18

B

14

C

11

D

25

E

24

F

17

G

14

H

10

I

23

J

11

K

22

L

19

Significant Level- P=0.05
Activities on daily living is denoted by ADL in the analysis
One-Sample Statistics


N

Mean

Std. Deviation

Std. Error Mean

ADL

12

17.33

5.365

1.549

One-Sample Test


Test Value = 17


t

df

Sig. (2-tailed)

Mean Difference

95% Confidence Interval of the Difference






Lower

Upper

ADL

.215

11

.834

.333

-3.08

3.74

The average number of activities on daily living (ADL) is 17.33 at p= .834. We therefore fail to reject the null hypothesis since the significant value is greater 0.05 (p> .05).
Significant Level- P=0.01
One-Sample Statistics


N

Mean

Std. Deviation

Std. Error Mean

ADL

12

17.33

5.365

1.549

One-Sample Test


Test Value = 17


t

df

Sig. (2-tailed)

Mean Difference

99% Confidence Interval of the Difference






Lower

Upper

ADL

.215

11

.834

.333

-4.48

5.14

The average number of activities on daily living (ADL) is also 17.33 at p= .834. We therefore fail to reject the null hypothesis since the significant value is greater 0.05 (p> .05).
Therefore, the average number of activities of daily living obtained after therapy is significantly different from a mean number of activities of 17 (typical for depressed people) at both .05 and .01 significance levels.
Mock Study 2: t- Test for Dependent Means
Research hypothesis
Null hypothesis
H0: The observed differences in the numbers of activities of daily living obtained before and after therapy are statistically significant.
Alternative Hypothesis
H1: The observed differences in the numbers of activities of daily living obtained before and after therapy are not statistically significant.
This study mock uses .05 significance level to test the hypotheses
The following data is uploaded onto IBM SPSS 24 for analysis:
CLIENT

BEFORE THERAPY

AFTER THERAPY

A

11

17

B

7

12

C

10

12

D

13

21

E

9

16

F

8

17

G

13

17

H

12

8

Paired Samples Statistics


Mean

N

Std. Deviation

Std. Error Mean

Pair 1

ADLPRE

10.38

8

2.264

.800


ADLPOST

15.00

8

4.071

1.439

Paired Samples Correlations


N

Correlation

Sig.

Pair 1

ADLPRE & ADLPOST

8

.248

.554

Paired Samples Test


Paired Differences

t

df

Sig. (2-tailed)


Mean

Std. Deviation

Std. Error Mean

95% Confidence Interval of the Difference








Lower

Upper




Pair 1

ADLPRE - ADLPOST

-4.625

4.138

1.463

-8.085

-1.165

-3.161

7

.016

The from the tables above, the average numbers of activities of daily living before therapy (ADLPRE) is 10.38 against the average numbers of activities of daily living after therapy which is 15. The significant level is .016. We, therefore, reject the null hypothesis and accept the alternative hypothesis since the p< 0.05. Therefore, the observed differences in the numbers of activities of daily living obtained before and after therapy are not statistically significant at p=0.05.
Mock Study 3: t-Test for Independent Samples
Research hypothesis
Null Hypothesis:
H0: The job satisfaction scores of the group that participated in counseling session are statistically different from the scores of employees who chose not to participate in counseling sessions
Alternative Hypothesis
H1: The job satisfaction scores of the group that participated in counseling session are not statistically different from the scores of employees who chose not to participate in counseling sessions
This study mock uses .01 significance level to test the hypothesis hypotheses
The following data is uploaded onto IBM SPSS 24 for analysis:
PARTICIPATED IN COUNSELING

DID NOT PARTICIPATE IN COUNSELING

36

38

39

36

41

36

36

32

37

30

35

39

37

41

39

35

42

33

Group Statistics


group

N

Mean

Std. Deviation

Std. Error Mean

ADL

PARTICIPATED IN COUNSELING

9

38.00

2.398

.799


DID NOT PARTICIPATE IN COUNSELING

9

35.56

3.504

1.168

Independent Samples Test


Levene's Test for Equality of Variances

t-test for Equality of Means


F

Sig.

t

df

Sig. (2-tailed)

Mean Difference

Std. Error Difference

99% Confidence Interval of the Difference