In placebo-controlled trials of Prozac , a drug that is prescribed to fight depr
ID: 2954888 • Letter: I
Question
In placebo-controlled trials of Prozac , a drug that is prescribed to fight depression, 23% of the patients who were taking the drug experienced nausea, whereas 10% of the patients who were taking the placebo experienced nausea.* If 50 patients who are taking Prozac are selected, what is the probability that 10 or more will experience nausea? Of the 50 patients in part a, what is the expected number of patients who will experience nausea? If a second group of 50 patients receives a placebo, what is the probability that 10 or fewer will experience nausea? If a patient from a study of 1000 people, who are equally divided into two groups (those taking a placebo and those taking Prozac ), is experience nausea, what is the probability that he/she is taking Prozac ? Since .23 is more than twice as large as. 10, do you think that people who take Prozac are more likely to experience nausea than those who take a placebo? Explain.Explanation / Answer
p(n|p).01 [probability of having nausea given the individualis taking the placebo]a. p(x>=10) = 1- p(x<9) so this can be treated as abinomial distribution p(i)=(n choosei)pi(1-p)n-i n choose i is n!/i!(n-i)! so you calculate 1- [p(x=0)+p(x=1)+p(x=2)....p(x=9) 1-[(50 choose 0)(.23)0(.77)50)+ (50choose 1)(.23)1(.77)49+.....(50 choose9)(.23)9(.77)41
b. e(x) = (number of patients)(probability) (50)(.23) = 11.5
c you do the same thing as before. but since this says 10 orfewer experiences nausea, p(x<=10) P(x=0)+P(x=1)+....+P(x=10)
d. P(d|n) = ? this is a simple bayes law formula problem since they are divided into equal group p(d)=p(p)=.5 P(d|n) = P(n|d)P(d)/[(P(n|d)P(d)+P(n|p)P(p)]
P(d|n)= (.23)(.5)/[(.23)(.5)+(.1)(.5)]
e. yes. given that an individual is taking prozac, theprobability that they will experience nausea is .23 or 23/100.given a person taking the placebo , the probability that they willexperience nausea is .1 or 10/100. they will not experiences nauseamore or less often, because in this problem it is something that anindividual experiences or does not experience.