collected for use in the approval process required by the
U.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
aWhat is the probability that 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?
a) prob = 47/69
b) prob = 20/51
c) prob = 67/120
Unless I am missing something, this looks pretty straightforward.
To find the probabilities in this scenario, you need to use the data given in the table and apply some basic probability concepts.
a. To find the probability that participants perceived that their "medication" helped if they received the drug, you need to consider the number of participants who received the drug and reported help, compared to the total number of participants who received the drug.
From the table, we can see that 47 participants who received the drug reported help. The total number of participants who received the drug is 22 (No Help) + 47 (Help) = 69.
Therefore, the probability that participants perceived that their "medication" helped if they received the drug is 47/69, which simplifies to approximately 0.6812 or 68.12%.
b. To find the probability that participants perceived that their "medication" helped if they received the placebo, you need to consider the number of participants who received the placebo and reported help, compared to the total number of participants who received the placebo.
From the table, we can see that 20 participants who received the placebo reported help. The total number of participants who received the placebo is 31 (No Help) + 20 (Help) = 51.
Therefore, the probability that participants perceived that their "medication" helped if they received the placebo is 20/51, which simplifies to approximately 0.3922 or 39.22%.
c. To find the probability that participants perceived that their "medication" helped, regardless of whether they received the drug or the placebo, you need to consider the total number of participants who reported help, compared to the total number of participants.
From the table, we can see that there are 47 participants who received the drug and reported help, and 20 participants who received the placebo and reported help. The total number of participants who reported help is 47 + 20 = 67.
The total number of participants is 22 (Drug - No Help) + 47 (Drug - Help) + 31 (Placebo - No Help) + 20 (Placebo - Help) = 120.
Therefore, the probability that participants perceived that their "medication" helped is 67/120, which simplifies to approximately 0.5583 or 55.83%.