In the tests of a new pharmaceutical product, data were collected for use in the approval process required by theU.S. Food and Drug Administration (FDA). Some participants were given a placebo, an inert substance that looks like the drug; others were given the drug. The data are shown in the following table:
No Help Help
Drug 22 47
Placebo 31 20
What is the probability that
a. the participants perceived that their “medication" helped if they received the drug?
b. the participants perceived that their “medication” helped if they received the placebo?
c. the participants perceived that their “medication” helped?
Add up all of the participants in your study. 22+47+31+20= 120
Formula: Part/whole= percentage
(a) 47 perceived help from drug. 47/120= .3917= 39%
(b) 20/120= .166, round to 16.7%
(c) 47+20= 67/120= .5583= 55.8%
a. 47/69 (only of those who got the drug)
b. 20/51 (only of those who got the placebo)
c. Yes
To determine the probability in each scenario, you need to calculate the conditional probability. Conditional probability calculates the probability of an event occurring given that another event has already occurred. In this case, the "No Help" and "Help" are the two events, and the drug or placebo is the condition.
a. To calculate the probability that participants perceived that their medication helped if they received the drug, you need to find the probability of "Help" given the drug. In this case, there were 47 participants who received the drug and perceived help.
So, the probability that participants perceived that their medication helped if they received the drug is calculated as:
Probability (Help | Drug) = Number of Help given Drug / Total number of participants who received the drug
Probability (Help | Drug) = 47 / (22 + 47)
b. To calculate the probability that participants perceived that their medication helped if they received the placebo, you need to find the probability of "Help" given the placebo. In this case, there were 20 participants who received the placebo and perceived help.
So, the probability that participants perceived that their medication helped if they received the placebo is calculated as:
Probability (Help | Placebo) = Number of Help given Placebo / Total number of participants who received the placebo
Probability (Help | Placebo) = 20 / (31 + 20)
c. To calculate the probability that participants perceived that their medication helped, you need to consider both the scenarios where participants received the drug and the placebo.
So, the probability that participants perceived that their medication helped is calculated as:
Probability (Help) = (Number of Help given Drug + Number of Help given Placebo) / Total number of participants
Probability (Help) = (47 + 20) / (22 + 47 + 31 + 20)
Please plug in the values and calculate the probabilities accordingly.