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 429 patients who took one brand of pain reliever, 23 suffered some "adverse symptom." Does the experiment provide strong evidence that fewer than 8% of patients who take this medication have adverse symptoms? (a) H_0: 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 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 429 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 5.36% of arthritis patients taking the pain medication experience adverse symptoms.

Explanation / Answer

Given that,
possibile chances (x)=23
sample size(n)=429
success rate ( p )= x/n = 0.0536
success probability,( po )=0.08
failure probability,( qo) = 0.92
null, Ho:p=0.08
alternate, H1: p<0.08
level of significance, = 0.05
from standard normal table,left tailed z /2 =1.64
since our test is left-tailed
reject Ho, if zo < -1.64
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.05361-0.08/(sqrt(0.0736)/429)
zo =-2.0146
| zo | =2.0146
critical value
the value of |z | at los 0.05% is 1.64
we got |zo| =2.015 & | z | =1.64
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: left tail - Ha : ( p < -2.01455 ) = 0.02198
hence value of p0.05 > 0.02198,here we reject Ho
ANSWERS
---------------
null, Ho:p=0.08
alternate, H1: p<0.08
test statistic: -2.0146
critical value: -1.64
decision: reject Ho
p-value: 0.02198

The data does provide statistical evidenoe at the 0.05 significance level that fewer than 8% of arthritis patients taking the
medication experience adverse symtoms

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