In this experiment, which of the following are valid null and alternative hypotheses statements for the factor of interest if analyzed using ANOVA? Select all that apply. Read the choices very carefully.  

If the appropriate t-test is used to analyze the data, the square of the t-statistic will be exactly equal to the F-statistic for the treatment effect in the RCBD ANOVA i.e., .

If we performed the appropriate t-test to analyze the data, the standard error (SE) used in that test and the Mean Square Error (MSE) from the RCBD ANOVA would be related in which of the following ways?  Hint: You can figure out the relationship by first calculating the standard error from the t-test and the MSE from ANOVA separately, and then comparing them.

If this experiment is analyzed as a completely randomized design (CRD), what is the error degrees of freedom?  Enter only the numeric value — no units, symbols, or text.  

If this experiment is analyzed as a randomized complete block design (RCBD), what is the error degrees of freedom?  Enter only the numeric value — no units, symbols, or text.  

There are true replicates in this experiment. 

The appropriate randomization scheme in this experiment is similar to that of a randomized complete block design.

For the next two questions, use the following case as context: A popular dietary supplement is being tested for efficacy. Twenty individuals were enlisted as test subjects and each individual was randomly assigned to one of two test groups — the placebo group and the treatment group. Both groups received a pill but only 10 of those were true dietary supplements (the other 10 are placebo pills).  

If a t-test was used to analyze the data, what would be the total number of degrees of freedom for the test?

In the residuals vs. observation number/run order/time plot after ANOVA, the residuals show a strong increasing (monotonic) trend. Which assumption on the error terms is most likely violated?