The samples from the two populations (Angus and Simmental) must be random and independent is not an assumption for Analysis of Variance (ANOVA). ANOVA only requires normally distributed populations with equal variances. Hence the correct option is c.
Assumptions of ANOVA:
Normality: Both populations (Angus and Simmental) should have approximately normal distributions for frame scores. This condition affects the validity of the F-statistic used in ANOVA.
Homogeneity of variances: The variances of the frame scores in both populations should be roughly equal. Violation of this assumption can affect the accuracy of F-statistic but doesn't directly invalidate the test.
Random and independent samples:
This requirement belongs to the realm of external validity, meaning it ensures your sample results can be generalized to the larger population. However, even with non-random or dependent samples, the ANOVA calculations within the specific data set will still provide an F-statistic and p-value.
Therefore, while random and independent samples are crucial for reliable research and drawing accurate conclusions, they are not specific assumptions of the ANOVA analysis itself. The test remains valid for calculating the F-statistic and p-value, though the conclusions drawn from those results might be biased or unreliable if the samples are not representative of the population or influenced by unknown dependencies. Hence the correct option is c.