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# Statistic (Statistics Project Sample)

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Homework #6
Independent sample data
The endurance scores of two independent groups of patients are as indicated in the following table. The patients in the treatment group were randomly assigned the synthetic hormone, erythropoietin or EPO, while those in the control group were assigned a neutral harmless substance.
Table SEQ Table \* ARABIC 1
ID
Score
Group (1=EPO, 2 =Control)
1
12
1
2
5
1
3
11
1
4
11
1
5
9
1
6
18
1
7
7
2
8
3
2
9
4
2
10
6
2
11
3
2
12
13
2
The independent sample t-test is the appropriate test to use in evaluating the effect of the synthetic hormone, erythropoietin or EPO on the endurance level. Using the independent t-test, the average endurance scores of the two independent groups are compared to determine whether they differ significantly. The results of the independent sample t-test used to compare the endurance scores of the treatment group and the control group are as follows.
Group Statistics
Group
N
Mean
Std. Deviation
Std. Error Mean
Score
EPO
6
11.00
4.243
1.732
Control
6
6.00
3.795
1.549
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
95% Confidence Interval of the Difference
Lower
Upper
Score
Equal variances assumed
.000
1.000
2.152
10
.057
5.000
2.324
-.178
10.178
Equal variances not assumed
2.152
9.878
.057
5.000
2.324
-.186
10.186
The null and alternative hypotheses used to evaluate the mean difference between the two independent groups are as stated below.
H0: Average endurance scores of the EPO group and control group are equal.
H1: Average endurance scores of the EPO group and control group differ.
Significance level, a = 0.05
The obtained t-value from the independent t-test is 2.152. The p-value (Sig. 2-tailed) derived also from the independent t-test is p = 0.057. This p-value is greater than the 0.05 significance level. Therefore, we fail to reject the null hypothesis and conclude that there is no significant difference between the average endurance scores of the EPO group and the control group. The results obtained from the independent t-test indicate no significant differences between the average endurance scores of the two independent groups. This implies that patients do not have better endurance when they dope using synthetic hormone, erythropoietin or EPO.
Paired samples data
The following table indicates the endurance scores of patients who were assigned to both the treatment and controlled conditions. The endurance level of each patient was measured twice; once under EPO treatment condition and the second time under controlled conditions.
Table SEQ Table \* ARABIC 2
ID2
Doped
Not doped
1
12
7
2
5
3
3
11
4
4
11
6
5
9
3
6
18
13
The paired sample t-test is the appropriate test to evaluate the effect of the synthetic hormone, erythropoietin or EPO on the endurance level. The results of the paired sample t-test are indicated as follows.
Paired Samples Statistics
Mean
N
Std. Deviation
Std. Error Mean
Pair 1
Doped
11.00
6
4.243
1.732
Not doped
6.00
6
3.795
1.549
Paired Samples Correlations
N
Correlation
Sig.
Pair 1
Doped & Not doped
6
.919
.010
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
Doped – Not doped
5.000
1.673
.683
3.244
6.756
7.319
5
.001
The following are the null and alternative hypotheses used to evaluate the effect of EPO treatment on the endurance level of patients who participated in...

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