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 442 patients who took one brand of pain reliever, 21 suffered some "adverse symptom." Does the experiment provide strong evidence that fewer than 8% of patients who take this medication have adverse symptoms?


(b) The test statistic is (Use 2 decimal places)

(c) The p-value is (Use 4 decimal places)

(d) Therefore, we can conclude that

a. The data does provide statistical evidence at the 0.05 significance level that fewer than 8% of arthritis patients taking the pain medication experience adverse symptoms.

b. The data does provide statistical evidence at the 0.05 significance level that fewer than 8% of these 442 arthritis patients taking the pain medication experience adverse symptoms.

c. The data does not provide statistical evidence at the 0.05 significance level that fewer than 8% of arthritis patients taking the pain medication experience adverse symptoms.

d. The data does provide statistical evidence at the 0.05 significance level that 4.75% of arthritis patients taking the pain medication experience adverse symptoms.

Answer 1

Step 1

Ho:

Ha:

Ho: The percentage of patients who take the medication and have adverse sympotoms is greater than or equal to 8%

Ha: The percentage of patients who take the medication and have adverse sympotoms is fewer than 8%

Step 2

n = 442

x = 21

z = -2.518

(b) Test statistics = -2.52

At significance level is α=0.05, and the critical value for a left-tailed test is zc = −1.64

As z stat falls in the rejection area, we reject the Null hypothesis.

p value

P ( Z<−2.518 )=1−P ( Z<2.518 )=1−0.9941=0.0059

As p value (0.0059) is less than  α=0.05, we reject the Null hypothesis.

(c) p value = 0.0059

(d) a. The data does provide statistical evidence at the 0.05 significance level that fewer than 8% of arthritis patients taking the pain medication experience adverse symptoms.