Final answer:
The question involves finding critical values for the F-distribution at different degrees of freedom for an alpha level of 0.05, using an F-distribution table or statistical software. The response outlines the process for determining these critical values and how they are used in hypothesis testing.
Step-by-step explanation:
The student's question is about finding the critical values of the F-distribution for given degrees of freedom at the alpha level of 0.05. These critical values are typically found in statistical tables or by using statistical software. The degrees of freedom in the numerator (dfnum) and denominator (dfdenom) are specified alongside the alpha level to determine the critical F value.
For F2,16, this would be the critical value of the F-distribution with 2 and 16 degrees of freedom, respectively. Similarly, for F4,16, it would be the critical value with 4 and 16 degrees of freedom. Lastly, for F4,36, it would be with 4 and 36 degrees of freedom.
Since the exact critical values are not provided here, you would refer to an F-distribution table or use statistical software to find:
- F2,16 at α = 0.05,
- F4,16 at α = 0.05, and
- F4,36 at α = 0.05.
The decision to reject the null hypothesis is made if the calculated F statistic is greater than the respective critical value at the given alpha level.