**Algebra 2 Segment 2 Honors Project**

By Emily Jones

By Emily Jones

Task Three

Okay…now it’s your turn!

Use your knowledge of fair decision making and probability concepts to analyze the product testing of the Power Pill and complete Task 3.

**Task One**

Task Two

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:

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 1:

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

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.

Part 2:

Part 3:

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.

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 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.

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

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:

By using the combination formula, since order does not have any significance in this situation, I found that there are 847,660,528 ways that these participants can be selected.

Due to the fact that doctors can only can hold one office on the research board, order does matter so we would have to use the permutation formula. By using this and substituting in proper values we can find that there are 32,760 ways to choose the research board.

Group A (told effects & medication)

Group B (not told effects & medication

Group C (told effects & placebo)

Group D (not told effects & placebo)

Total

Total

Saw results

Did not see results

6 (15%)

4 (10%)

10

10

10

10

40

7 (17.5%)

5 (12.5%)

4 (10%)

22

18

3 (7.5%)

5 (12.5%)

6 (15%)

The probability that a person saw results, given that they received the Power Pill is 65%. The probability that someone saw results, given they received a placebo is 45%. I figured this out using conditional probability.

Given that someone did not see results, the probability of them receiving a placebo is 55%. Given that that they did not see results, the probability of them receiving the Power Pill is 35%.

The Power Pill is a medication that, given the results of the experiment, should be produced and distributed. This is due to the fact that rules of a fair experiment were followed including ensuring that there was randomization.

The Power Pill appeared to show more results in people if they were not told about the effects. This is proven by the fact that if they weren't told, then the success rate of the Power Pill is 70% compared to if they were told is only 60%. This is the opposite for the placebo where if told, success rate is 50% compared to where if not told success is only 40%.

The only flaw found was that while there is technically a control group (the one given the placebo), a placebo actually could have an effect on participants in that group. So maybe try to include a control group where they are given nothing to measure normal hair growth.