**End**

Start

Task 1:

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.

By using the combination formula you can determine that there are 847,660,528 ways to pick participants.

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.

There is 37,760 ways to choose the research board because each person can only have one position.

Task 2

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.

The probability is 55% that someone saw results and the probability is 45% that someone saw results with placebo.

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.

The probability that someone did not see results with power pill is 39%. And for the people that used placebo the people that did not see results was 61%.

**Segment Two Honors Project**

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.

Yes. Having a control group would have bettered the experiment.

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.

If the person was not told then the results were better and the percentages back up my claim.

Task 3

Part 1:

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

Yes, because the results show that the people saw more results than they did not see results.