Question

A new drug has been developed to treat a particular condition, and it is alleged to be more effective than traditional treatment. An experiment will be conducted to test whether the claim is true. To perform the hypothesis test, a 99% confidence level is selected for the hypothesis test. The new drug will be administered to a sample of 200 individuals with the condition, selected at random. Another 300 individuals are randomly selected to receive the traditional treatment.

Of the 200 individuals treated with the new drug, 140 were completely cured. Of those treated with the traditional method, 160 were completely cured.

a. Is there statistical evidence to support the claim that the new drug is more effective? Take the proper test and finish. 16 pts

b. If you were a patient of this condition, which treatment would you select? Justify your answer 9 pts

Answer 1

Given that,
sample one, x1 =140, n1 =200, p1= x1/n1=0.7
sample two, x2 =160, n2 =300, p2= x2/n2=0.533
null, Ho: p1 = p2
alternate, H1: p1 > p2
level of significance, α = 0.01
from standard normal table,right tailed z α/2 =2.326
since our test is right-tailed
reject Ho, if zo > 2.326
we use test statistic (z) = (p1-p2)/√(p^q^(1/n1+1/n2))
zo =(0.7-0.533)/sqrt((0.6*0.4(1/200+1/300))
zo =3.727
| zo | =3.727
critical value
the value of |z α| at los 0.01% is 2.326
we got |zo| =3.727 & | z α | =2.326
make decision
hence value of | zo | > | z α| and here we reject Ho
p-value: right tail - Ha : ( p > 3.7268 ) = 0.0001
hence value of p0.01 > 0.0001,here we reject Ho
ANSWERS
---------------
a.
null, Ho: p1 = p2
alternate, H1: p1 > p2
test statistic: 3.727
critical value: 2.326
decision: reject Ho
p-value: 0.0001
we have enough evidence to support the claim that the new drug is more effective.
b.
yes,
A new drug has been developed to treat a particular condition, and it is alleged to be more effective than traditional treatment.
An experiment will be conducted to test whether the claim is true. To perform the hypothesis test is Z test for difference of proportion.