An experiment on the side effects of pain relievers assigned

An experiment on the side effects of pain relievers assigned arthritis patients to take one of several over-the-counter pain medications. Of the 436 patients who took one brand of pain reliever, 25 suffered some \"adverse symptom.\" Does the experiment provide strong evidence that fewer than 12% of patients who take this medication have adverse symptoms?

(a) H₀: 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 436 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 that 5.73% of arthritis patients taking the pain medication experience adverse symptoms.

Solution

Given that an experiment on the side effects of pain relievers assigned arthritis patients to take one of several over-the-counter pain medications.

number of suffered some \"adverse symptom.\" (x) = 25

number of patients who took one brand of pain reliever (n) = 436

Here we want to test the hypothesis that,

H₀ : p = 0.12 Vs H₁ : p < 0.12

given that level of significance () = 0.05

the test statistic for that is,

z = (p^ - p) / sqrt (pq/n)

sample proportion (p^) = x / n = 25 / 436 = 0.0573

p = 0.12

q = 1 - p = 1 - 0.12 = 0.88

z = (0.0573 - 0.12) / sqrt [ (0.12*0.88) / 436 ] = -0.06266 / 0.015563 = -4.03

We can calculate p-value in EXCEL using command ,

P-value = normsdist(-4.03) = 0.0000

Since P-value <

Reject H₀ at 5% level of significance.

Conclusion :  The data does provide strong evidence at the 0.05 significance level that fewer than 12% of patients arthritispatients taking the pain medication experience adverse symptoms.