Hypothesis testing

Suppose a pharmaceutical company claims that their allergy medicine is 90% effective in relieving allergies for a 12-hour period. To test that claim, an independent laboratory conducts an experiment with 200 subjects. Of them, only 160 report that the medicine was, as claimed, effective against allergies for 12 hours. The laboratory must determine whether that data is sufficient to reject the company's claim.

To set up the analysis, we first identify the population, the random sample, the relevant random variable, its distribution, and the hypothesis to be tested. In this case, the population could be all potential consumers of the medicine, the random sample is the set of n = 200 subjects reporting their results, and the random variable X is the number of those who did get the promised allergy relief. This random variable has the binomial distribution, with p being the probability that any one person does get that relief from taking the medicine. Finally, the hypothesis...