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 430 patients who took one brand of pain reliever, 24 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

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 430 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 5.58% of arthritis patients taking the pain medication experience adverse symptoms.

Answer 1

Solution :

Given that,

= 8% = 0.08

1 - = 1 - 0.08 = 0.92

n = 430

x = 24

Level of significance = = 0.05

Point estimate = sample proportion = = x / n = 24 / 430 =

This a left (One) tailed test.

a)

Ho: p = 0.08

Ha: p < 0.08

b)

Test statistics

z = ( - ) / *(1-) / n

= ( 0.0558 - 0.08) / (0.08*0.92) / 430 = 0.0558

= -1.85

c)

P-value = P(Z < z)

= P(Z < -1.85)

= 0.0322

The p-value is p = 0.0322, and since p = 0.0322 < 0.05, it is concluded that the null hypothesis is rejected.

Conclusion:

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