Question: Suppose that you conduct a study to determine the effects of four treatments (A, B, C, and D) on several responses. Some responses are continuous random variables (e.g., the weight loss of individuals during the time of the study) while other responses are discrete random variables (e.g., four categories of agreement – Strongly Disagree, Disagree, Agree, and Strongly Agree).

1. Describe how you would design the study in a completely randomized way. Your description should include considerations on how to randomly assign treatments to individuals/units.
2. Suppose that there are three hospitals that will be considered blocks. Describe how you would design the study in a completely randomized block design. Your description should include considerations on how to randomly assign treatments to individuals/units that is clearly different from part a.
3. For the continuous random variable responses, describe the type of analysis that should be conducted to determine if at least one of the treatments has a different average response, including example null and alternative hypotheses. And then write Why you would use this specific type of analysis?

1. For the discrete random variable responses, describe the type of analysis that should be conducted to determine if there is an association between the four treatments and the response categories, including example null and alternative hypotheses. And then write Why you would use this specific type of analysis?

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