**Algebra 2 Honors Project**

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.

There are 847,660,528 different ways to select participants. I found this by doing the combination formula on the group since it does not matter how they are selected.

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 are 32,760 different ways to choose the research board. Because each person can only hold one position the permutation formula was needed and this is the result.

Task 1

The first task of the Segment Two Honors Project is to select the Power Pill study participants’ groups and research board officers.

Task 2 (continued)

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:

Six in Group A saw results.

Seven in Group B saw results.

Five in Group C saw results.

Four in Group D saw results.

Task 2

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.

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.

Part 1

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

Group A Group B Group C Group D Total

Saw Results 6 7 5 4 22

Saw no 4 3 5 6 18

Results

Total 10 10 10 10 40

Part 1 Continued

Given the results of this test we can find that if you chose a random person the chances to pick the following are:

Group A (Results): 15%

Group A (No Results): 10%

Group B (Results): 17.5%

Group B (No Results): 7.5%

Group C (Results): 12.5%

Group C (No Results): 12.5%

Group D (Results): 10%

Group D (No Results): 15%

Drug & told effects Drug & not told effects Placebo & told effects Placebo & not told effects

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.

Based on the results the probability that a person saw results with the pill is 55%, and the probability that a person saw results with the placebo is 45%.

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 a person did not see results and given the power pill is approximately 38.9% and for the people who received the placebo and did not see results is approximately 61.1%

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, I believe the drug should be distributed. The tests subjects were all completely randomized and there was mostly a higher percentage of people who saw the results even when given no information, the placebo, or both.

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.

It seemed that if the person got the pill and wasn't told, than the pill worked better and if the person got the placebo and was told the pill worked better. The percentages for these groups back me up. If the person received information and the pill, the percentage (in each of their respected groups) was 60%. But if they weren't told than the success rate was 70%! And if the placebo group was told the rate was 50% and if they were left in the dark it was only 40%.

Task 3 (Continued)

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.

They need to have a control group where absolutely nothing is given to them. They can than take the results of hair growth from that group to compare with.