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 449 patients who took one brand of pain reliever, 25 suffered some "adverse symptom." Does the experiment provide strong evidence that fewer than 8% of patients who take this medication have adverse symptoms?

(a) H₀: p  ---Select--- < > =  and H_a: p  ---Select--- ≠ < ≥ ≤ > =  

(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 8% 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 8% of these 449 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 8% of arthritis patients taking the pain medication experience adverse symptoms.

The data does provide statistical evidence at the 0.05 significance level that 5.57% of arthritis patients taking the pain medication experience adverse symptoms.

Answer 1

a) H₀: P = 0.08

    H₁: P < 0.08

b) = 25/449 = 0.06

The test statistic z = ( - P)/sqrt(P(1 - P)/n)

                             = (0.06 - 0.08)/sqrt(0.08 * (1 - 0.08)/449)

                             = -1.56

c) P-value = P(Z < -1.56)

                 = 0.0594

d) As the P-value is greater than the significance level (0.0594 > 0.05), so we should not reject the null hypothesis.

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