Final answer:
The decision about the null hypothesis in an ANOVA test depends on whether the calculated F-ratio is greater than the critical value from the F-distribution table for the given degrees of freedom and alpha level. If the calculated F-ratio of 3.30 is greater than the critical value, the null hypothesis is rejected.
Step-by-step explanation:
The student is asking about making a decision related to the null hypothesis in the context of an ANOVA (Analysis of Variance) test. The F-ratio calculated at 3.30 needs to be compared to a critical value from the F-distribution table based on the degrees of freedom and the chosen level of significance, known as alpha (α). If the calculated F-ratio is greater than the critical value, we reject the null hypothesis; if it is less than or equal to the critical value, we fail to reject the null hypothesis.
Assuming the study is using a common α level such as 0.05, and given the degrees of freedom (df) for the numerator (k-1, where k is the number of groups) and the denominator (N-k, where N is the total number of observations), df1 would be 4-1=3, and df2 would be 16-4=12. The decision to reject or not reject the null hypothesis would be based on the critical F-value for df1=3 and df2=12 at α=0.05. If the calculated F-ratio of 3.30 is higher than the critical value from the F-distribution table, then the decision would be to reject the null hypothesis, implying that there is sufficient evidence to suggest that at least one group mean is different from the others.