Question 1182750: The probability of flu symptoms for a person not receiving any treatment is 0.057. In a clinical trial of a common drug used to lower cholesterol, 68 of 1118 people treated experienced flu symptoms. Assuming the drug has no effect on the likelihood of flu symptoms, estimate the probability that at least 68 people experience flu symptoms. What do these results suggest about flu symptoms as an adverse reaction to the drug?
P(X ≥ 68) = __(Round to four decimal places as needed.)
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! In other words, how likely is it that of 1118 people, 68 will get flu symptoms given that the probability is 0.057?
68/1118=0.0608
1-sample proportion test
Ho: true proportion is < =0.057
Ha: true proportion is >0.057 (in other words, something has changed the proportion, like the drug)
alpha=0.05 p{reject Ho|Ho true}
critical value is z>1.645
z=(0.0608-0.057)/sqrt(p*(1-p)/n)
=0.0038/sqrt(0.057*0.943/1118); sqrt term=0.0069
=0.0038/0.0069
=0.548
probability z>0.548 is 0.2918
There is insufficient evidence to conclude that the drug is producing these side effects. We failed to reject the null hypothesis, and the p-value is 0.2918, meaning that if the null hypothesis were true, we would have a 29.2% chance of finding a result this much or more extreme.
==
normal approximation
np=63.726=mean
np(1-p)=60.093=variance
sd= sqrt(V)=7.75
probability the value is above 68
z=(68-63.7)/7.75=0.5548; that probability is 0.2895
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