U VIII
Running head: TEST AND ANOVA SUN COAST 1
Test and ANOVA Sun Coast Remediation Data Set
Student’s Name
Instructor’s Name
Course
Date
Data Analysis: Hypothesis Testing
This assignment involves using the Sun Coast Remediation data set to perform statistical tests, in particular, independent samples t test, dependent samples (paired samples) t test as well as ANOVA test. The statistical tables are illustrated.
Independent Samples t Test: Hypothesis Testing
H04: There is no statistically significant difference in variance values for training scores between Group A and Group B.
HA4: There is statistically significant difference in variance values for training scores between Group A and Group B.
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Variable 1 |
Variable 2 |
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Mean |
69.79032 |
84.77419 |
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Variance |
122.0045 |
26.96457 |
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Observations |
62 |
62 |
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Hypothesized Mean Difference |
0 |
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df |
87 |
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t Stat |
-9.66656 |
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P(T<=t) one-tail |
9.7E-16 |
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t Critical one-tail |
1.662557 |
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P(T<=t) two-tail |
1.94E-15 |
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t Critical two-tail |
1.987608 |
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The results indicate that the variance values are lower for Group B. The p value is 1.94E-15 < 0.05 (Rumsey, 2011). Therefore, the null hypothesis is rejected and the alternative hypothesis accepted since there is statistically significant difference in variance values between Group A and Group B.
Dependent Samples (Paired Samples) t Test: Hypothesis Testing
H05: There is no statistically significant difference in mean values between pre-exposure and post-exposure.
HA5: There is statistically significant difference in mean values between pre-exposure levels and post-exposure levels.
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Variable 1 |
Variable 2 |
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Mean |
32.85714 |
33.28571 |
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Variance |
150.4583 |
155.5 |
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Observations |
49 |
49 |
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Pearson Correlation |
0.992236 |
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Hypothesized Mean Difference |
0 |
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df |
48 |
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t Stat |
-1.9298 |
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P(T<=t) one-tail |
0.029776 |
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t Critical one-tail |
1.677224 |
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P(T<=t) two-tail |
0.059553 |
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t Critical two-tail |
2.010635 |
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The results indicate that the mean values of pre-exposure and post-exposure are almost equal. The results further indicate a p value of 0.06 > 0.05 (Rumsey, 2011). Therefore, the null hypothesis is accepted since there is statistically significant difference in mean values of pre-exposure and post-exposure levels.
ANOVA: Hypothesis Testing
H06: There is no statistically significant difference in yield between means of the variables.
HA6: There is statistically significant difference in yield between means values of the variables.
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Anova: Two-Factor Without Replication |
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SUMMARY |
Count |
Sum |
Average |
Variance |
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Row 1 |
4 |
30 |
7.5 |
12.33333 |
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Row 2 |
4 |
29 |
7.25 |
14.25 |
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Row 3 |
4 |
29 |
7.25 |
14.91667 |
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Row 4 |
4 |
31 |
7.75 |
5.583333 |
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Row 5 |
4 |
25 |
6.25 |
4.916667 |
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Row 6 |
4 |
32 |
8 |
2.666667 |
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Row 7 |
4 |
33 |
8.25 |
6.916667 |
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Row 8 |
4 |
33 |
8.25 |
8.916667 |
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Row 9 |
4 |
25 |
6.25 |
2.25 |
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Row 10 |
4 |
31 |
7.75 |
3.583333 |
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Row 11 |
4 |
32 |
8 |
3.333333 |
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Row 12 |
4 |
32 |
8 |
6 |
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Row 13 |
4 |
25 |
6.25 |
4.916667 |
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Row 14 |
4 |
21 |
5.25 |
0.916667 |
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Row 15 |
4 |
22 |
5.5 |
4.333333 |
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Row 16 |
4 |
22 |
5.5 |
3 |
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Row 17 |
4 |
38 |
9.5 |
20.33333 |
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Row 18 |
4 |
38 |
9.5 |
4.333333 |
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Row 19 |
4 |
38 |
9.5 |
3.666667 |
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Row 20 |
4 |
42 |
10.5 |
9 |
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Column 1 |
20 |
178 |
8.9 |
9.357895 |
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Column 2 |
20 |
182 |
9.1 |
3.042105 |
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Column 3 |
20 |
140 |
7 |
6.631579 |
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Column 4 |
20 |
108 |
5.4 |
1.410526 |
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ANOVA |
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Source of Variation |
SS |
df |
MS |
F |
P-value |
F crit |
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Rows |
162.7 |
19 |
8.563158 |
2.162605 |
0.013126 |
1.771972 |
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Columns |
182.8 |
3 |
60.93333 |
15.38857 |
1.89E-07 |
2.766438 |
|
Error |
225.7 |
57 |
3.959649 |
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Total |
571.2 |
79 |
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Since the p values for rows is 0.01 < 0.05 the null hypothesis is rejected (Rumsey, 2011). Therefore, the alternative hypothesis is accepted.
Reference Rumsey, D. J. (2011). Statistics For Dummies. John Wiley & Sons.