Part 1:

There are 40 volunteers for the research study on the Power Pill. Each subgroup of the study will contain 10 participants. Determine how many ways these participants can be selected and explain your method.

Part 2:

There are 15 research doctors participating in the study and the research board needs to be established with the offices of director, assistant director, quality control analyst, and correspondent. (Doctors can only hold one office on the research board.) Determine how many ways this research board can be chosen and explain your process.

In Task 1, you selected the participants’ groups and assigned roles for the research board. For Task 2, you will now analyze the data collected from the groups.

The study participants were divided into four groups—two groups received the Power Pill (Group A and Group B) and two groups received a placebo (Group C and Group D). The effects of the Power Pill were measured. One group that received the Power Pill (Group A) and one group that received the placebo (Group C) were told of the anticipated effects of the Power Pill—accelerated hair growth—while the other two groups (Group B and Group D) were not provided with this information. All four groups were told to monitor and report any physical changes during the study.

Results were reported and participants were grouped as to either “Saw Results,” meaning that participants reported increased hair growth as part of physical changes during the study, or “No Results,” meaning that increased hair growth was not mentioned as part of physical changes during study.

Results are as follows:

6 in Group A saw results.
7 in Group B saw results.
5 in Group C saw results.
4 in Group D saw results.
Part 1:

Create a two-way table for the data and find the probabilities for each group. Describe results in terms of the study.

Part 2:

What is the probability that a person saw results, given they received the Power Pill? What is the probability that a person saw results, given they received a placebo? Explain in terms of the study.

Part 3:

What is the probability that a person received the placebo, given that they did not see results? What is the probability that a person received the Power Pill, given that they did not see results? Explain in terms of the study.

Part 1:

Based on your knowledge of fair decision making and probability concepts, should the Power Pill be produced and distributed? Explain your reasoning.

Part 2:

What effect (if any) did telling two groups about expected outcomes have on results? Use statistics to provide proof for your reasoning and explain.

Part 3:

Are there any flaws in the testing process? Should any of the steps or protocol be changed/avoided during round two of testing? Explain your reasoning.