An experiment on the side effects of pain relievers assigned arthritis patients

Question

An experiment on the side effects of pain relievers assigned arthritis patients to take one of several over-the-counter pain medications. Of the 448 patients who took one brand of pain reliever, 22 suffered some "adverse symptom." Does the experiment provide strong evidence that fewer than 12% of patients who take this medication have adverse symptoms? (a) H_0: p and H_a: p (b) The test statistic is (Use 2 decimal places) (c) The p-value is (Use 4 decimal places) (d) Therefore, we can conclude that (choose all that apply) The data does provide statistical evidence at the 0.05 significance level that fewer than 12% of arthritis patients taking the pain medication experience adverse symptoms. The data does provide statistical evidence at the 0.05 significance level that fewer than 12% of these 448 arthritis patients taking the pain medication experience adverse symptoms. The data does not provide statistical evidence at the 0.05 significance level that fewer than 12% of arthritis patients taking the pain medication experience adverse symptoms. The data does provide statistical evidence at the 0.05 significance level 4.91% of arthritis patients taking the pain medication experience adverse symptoms.

Explanation / Answer

a) Ho: po=0.12 ; Ha:po<0.12

std error =(po(1-po)/n)1/2 where n=448

=0.0154

phat=22/448=0.0491

b) hence test stat z=(phat-p)/std error =-4.62

p value =0.0000

d) the data does provide sufficient evidence at the 0.05 level that fewer then 12% of arthirits patient taking the pain medication experience adverse symptoms

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