(h) Using R-Studio, carry out relevant tests to determine if the assumptions of normality and homogeneity of variance were violated. Carefully discuss your findings quoting relevant statistics in your response and provide the necessary hypotheses. (Provide
Answer sub part H
h)
Data for the first store:
| Country\Box colour | Red | Yellow | Blue |
| A | 47 | 52 | 60 |
| B | 56 | 54 | 52 |
| C | 49 | 63 | 55 |
| D | 41 | 44 | 48 |
Normality assumption test:
Null Hypothesis:
H0: Normality assumption was not violated
Alternative Hypothesis:
H1: Normality assumption was violated.
R syntax:
From the output, the p value is 0.02882.
From the given information, .
Decision Rule:
If p-value ≤ α, then reject the null hypothesis.
Conclusion:
The level of significance is α=0.05
Here, the p-value is less than the level of significance.
From the decision rule, reject the null hypothesis.
Thus, Normality assumption was violated.
Homogeneity of variance test:
Null Hypothesis:
H0: Homogeneity of variance assumption was not violated
Alternative Hypothesis:
H1: Homogeneity of variance assumption was violated.
R syntax:
From the output, the p value for color group is 0.7827.
Conclusion:
The level of significance is α=0.05
Here, the p-value is greater than the level of significance.
From the decision rule, failed to reject the null hypothesis.
From the output, the p value for Country group is 0.4351
Here, the p-value is greater than the level of significance.
From the decision rule, failed to reject the null hypothesis.
Hence, the Homogeneity of variance assumption was not violated.
Thus, the normality assumption violated and Homogeneity of variance assumption was not violated for the ANOVA technique of first store data.
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