**Segment 2 Honors Project**

Task 3

**Algebra 2 - 10.07**

Task 2

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.

Task 1

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

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

It appears that the Power Pill worked better if the subject did not no the effects of the pill. If the person recived the Power Pill and information there is a 60% the drug worked. However, if the preson recived the Power Pill without the information there's a 70% chance the drug worked.

On the other hand, it seems that those who recived the placebo saw better results if they were told about the effects of the placebo. Amoung those who recived the placebo and were given information 50% of them saw results, while only 40% of those who didn't recive information saw results.

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.

In order to solve this question you can use the combination formula. This is because the order in which they are selected holds no importance. After substituting the values into the formula I got the answer, 847, 660, 528.

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 possible ways of choosing this research board. Since each person may only hold one position you are required to use the permutation formula,

Saw Results

Saw No

Results

Total

Group A

Group B

Group C

Group D

Total

6

7

5

4

10

10

10

10

40

22

4

3

5

6

18

Drug + Told Effects

Drug + Not Told Effects

Placebo + Told Effects

Placebo + Not Told Effects

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%

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 that a person saw results, given that they recived the Power Pill is 65%. The probability tat a person saw results, given that they recived the palcebo is 45%.

I arrived at an answer by using the table from the previous frame to inorder to provide vales to substitute into the formula P(A|B) = P(A & B) / P(B).

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 probablity that a person received that placebo, given that they did not see results is 38.9%. The probblity that a person recived the Power Pill given that they did not see results is 61.1%.

Part 1

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

I belive that the Power Pill should be produced and distributed. The groups were chosen randomly and equally. However, as I will explain in part 3, I think the experiment should be conducted again without telling the subjects the effects of the pill.

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.

I think the only major flaw that I would attempt to avoid, is telling the patients the effect of the pill. This result in bias and can effect the outcome.