An experiment on the side effects of pain relievers assigned arthritis patients to take one of several over-the-counter pain medications. Of the 440 patients who took one brand of pain reliever, 23 suffered some adverse symptom.

a. If 10% of all patients suffer adverse symptoms, what would be the sampling distribution of the proportion with adverse symptoms in a sample of 440 patients?

b. Does the experiment provide strong evidence that fewer than 10% of patients who take this medication have adverse symptoms? Verify that the conditions for inference are met. State the hypothesis, calculate the test statistic, then obtain and interpret the P-value.