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 442 patients who took one brand of pain reliever, 25 suffered some "adverse symptom." Does the experiment provide strong evidence that fewer than 10% of patients who take this medication have adverse symptoms?

(a) H0: p (<, >, or =) __________ and Ha: p (=, <, , , >, or ) ___________

(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 10% 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 10% of these 442 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 10% of arthritis patients taking the pain medication experience adverse symptoms.

The data does provide statistical evidence at the 0.05 significance level that 5.66% of arthritis patients taking the pain medication experience adverse symptoms.

Explanation / Answer

a) We can take as H0=0.10

and also take Ha<0.10 that's because the problem says that of the 442 patients who took one brand of pain reliever 25 suffered some "adverse symptom" and 25/442 is less than 0.10

b) If we take a statistic sample of 30 people assuming that the favorable cases are x<=3 that is the 10% of 30

If P^<0.1 we can discard H0 but if P^=0.1 we discard Ha.

Then we have this equation

P(X>=3 n=30, p=0,1) = 1 - 0,6475= 0.3525

it means that if we accept H0 we have 0.3525 probabilities to be right

P(X<3 n=30, p=0,1) = 1 - 0,4114= 0.5886

but if we accept Ha we have 0.5886 probabilities to be right

c) the p-value is

1 - 0.5886=0.4414

d)

the correct option is "The data does provide statistical evidence at the 0.05 significance level that fewer than 10% of arthritis patients taking the pain medication experience adverse symptoms."

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