Question

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 from 10 people in Group A saw results.•7 from 10 people in Group B saw results.•5 from 10 people in Group C saw results.•4 from 10 people 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.

Answer 1

Part 1.

First, let's create the two-way table for all the people that saw results:

Part 2:

The number of people that received a power pill is 20, and from these people, only 13 saw results, so the probability is 13/20 = 0.65 = 65%.

The number of people that received a placebo is 20, and from these people, only 9 saw results, so the probability is 9/20 = 0.45 = 45%.

That means if the person received a power pill, the probability of seeing results is greater.

Part 3:

The number of people that didn't see results is 18, and from these people, 11 received a placebo, so the probability is 11/18 = 0.6111 = 61.11%.

The number of people that didn't see results is 18, and from these people, 7 received a power pill, so the probability is 7/18 = 0.3889 = 38.89%.

That means if the person didn't see any results, the probability of having received a placebo is greater.