)Find the probability that the patient showed improvement.=P(improvement)0.32(b)Find the probability that the patient showed improvement, given that he took the new medication.=P(improvement | new medication)27(c)Is there evidence that a patient who takes the new medication is more likely to show improvement than a randomly chosen patient from th
Question
)Find the probability that the patient showed improvement.=P(improvement)0.32(b)Find the probability that the patient showed improvement, given that he took the new medication.=P(improvement | new medication)27(c)Is there evidence that a patient who takes the new medication is more likely to show improvement than a randomly chosen patient from th
Solution
It seems like you've accidentally cut off the end of your question, but I'll try to answer based on what you've provided.
(a) The probability that a patient showed improvement, denoted as P(improvement), is given as 0.32. This means that, out of all the patients in the study, 32% showed improvement.
(b) To find the probability that a patient showed improvement given that they took the new medication, denoted as P(improvement | new medication), we would need additional information. You've mentioned the number 27, but without context or a total number of patients who took the new medication, we can't calculate this probability.
(c) To determine if there's evidence that a patient who takes the new medication is more likely to show improvement than a randomly chosen patient, we would compare P(improvement | new medication) to P(improvement). If P(improvement | new medication) > P(improvement), then we could say there's evidence to suggest the new medication increases the likelihood of improvement. However, as mentioned in part (b), we don't have enough information to calculate P(improvement | new medication).
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