Out of 2,500 patients, 37 had adverse reactions to a drug

H0 :   π  =  0.01
HA :   π  >  0.01

Use this diagram to give an example of the use of a normal approximation to obtain a p-value. A simulation is used first to find an approximate p-value before the normal approximation is used.

Click Accumulate then simulate sampling of 2,500 patients about 300 times. (Hold down the button Simulate.)

Mention that using the binomial distribution would find the exact p-value but would involve summing a very large number of binomial probabilities.

Select Bar chart from the pop-up menu, then select Normal approximation to find the approximate p-value without a simulation.

Since the probability of 37 or more people getting adverse reactions is 0.0104, there is strong evidence that the probability of an adverse reaction is more than 0.01.


A pharmaceutical company claims that only 1% of the users of a certain drug experience adverse reactions. To test its claim, an agency monitors 2500 patients taking the drug and observes adverse reactions in 37 cases. Is the occurrence of adverse reactions more common than claimed by the company?