Subjects with pre-existing cardiovascular symptoms who were receiving subitramin
ID: 3231845 • Letter: S
Question
Subjects with pre-existing cardiovascular symptoms who were receiving subitramine, an appetite suppressant, were found to be at increased risk of cardiovascular events while taking the drug. The study included 9804 overweight or obese subjects with pre-existing cardiovascular disease and/or type 2 diabetes. The subjects were randomly assigned to subitramine (4905 subjects) or a placebo (4899 subjects) in a double-blind fashion. The primary outcome measured was the occurrence of any of the following events: nonfatal myocardial infarction or stroke, resuscitation after cardiac arrest, or cardiovascular death. The primary outcome was observed in 562 subjects in the subitramine group and 492 subjects in the placebo group.
Does the data give good reason to think that there is a difference between the proportions of treatment and placebo subjects who experienced the primary outcome?
State the hypotheses. Find the test statistic and the P-value. (Round test statistic to two decimal places and P-value to four decimal places.)
ptreatment = < > pplacebo
Z=
P value=
State your conclusion. (Use = 0.05.)
Because the P-value is large, we have evidence that there is a difference in the proportion of "primary outcomes" between subitramine and placebo.
Because the P-value is small, we have evidence that there is a difference in the proportion of "primary outcomes" between subitramine and placebo.
Because the P-value is small, we do not have evidence that there is a difference in the proportion of "primary outcomes" between subitramine and placebo.
Because the P-value is large, we do not have evidence that there is a difference in the proportion of "primary outcomes" between subitramine and placebo.
H0: ptreatment = < > pplacebo H1:ptreatment = < > pplacebo
Z=
P value=
State your conclusion. (Use = 0.05.)
Because the P-value is large, we have evidence that there is a difference in the proportion of "primary outcomes" between subitramine and placebo.
Because the P-value is small, we have evidence that there is a difference in the proportion of "primary outcomes" between subitramine and placebo.
Because the P-value is small, we do not have evidence that there is a difference in the proportion of "primary outcomes" between subitramine and placebo.
Because the P-value is large, we do not have evidence that there is a difference in the proportion of "primary outcomes" between subitramine and placebo.
Explanation / Answer
Given that,
sample one, x1 =562, n1 =4905, p1= x1/n1=0.115
sample two, x2 =492, n2 =4899, p2= x2/n2=0.1
null, Ho: p1 = p2
alternate, H1: p1 != p2
level of significance, = 0.05
from standard normal table, two tailed z /2 =
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic (z) = (p1-p2)/(p^q^(1/n1+1/n2))
zo =(0.115-0.1)/sqrt((0.108*0.892(1/4905+1/4899))
zo =2.261
| zo | =2.261
critical value
the value of |z | at los 0.05% is 1.96
we got |zo| =2.261 & | z | =1.96
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 2.2613 ) = 0.0237
hence value of p0.05 > 0.0237,here we reject Ho
ANSWERS
---------------
null, Ho: p1 = p2
alternate, H1: p1 != p2
test statistic: 2.261
critical value: -1.96 , 1.96
decision: reject Ho
p-value: 0.0237
Because the P-value is small, we have evidence that there is a difference in the
proportion of "primary outcomes" between subitramine and placebo