Question

Nex is a medicine that can be used to reduce the acid produced by the body and heals damage to the esophagus due to acid reflux. The manufacturer of Nex claims that over 94% of patients taking Nex are cured in 8 weeks. In clinical trials, 214 of 225 patients suffering from acid reflux disease were cured after 8 weeks. Test the manufacturer's claim at the significance level α = 0.05.

Answer the following:

Hypothesis test: Ho: p = Answer versus H1: p Answer Answer

Using the classical method: The test statistic (to two decimal places) is Answer.

The critical value is: Answer.

The decision is: Answer

Conclusion: Answer

Answer 1

Given that,
possibile chances (x)=214
sample size(n)=225
success rate ( p )= x/n = 0.951
success probability,( po )=0.94
failure probability,( qo) = 0.0600000000000001
null, Ho:p=0.94
alternate, H1: p>0.94
level of significance, α = 0.05
from standard normal table,right tailed z α/2 =1.645
since our test is right-tailed
reject Ho, if zo > 1.645
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.95111-0.94/(sqrt(0.0564)/225)
zo =0.702
| zo | =0.702
critical value
the value of |z α| at los 0.05% is 1.645
we got |zo| =0.702 & | z α | =1.645
make decision
hence value of |zo | < | z α | and here we do not reject Ho
p-value: right tail - Ha : ( p > 0.70179 ) = 0.2414
hence value of p0.05 < 0.2414,here we do not reject Ho
ANSWERS
---------------
null, Ho:p=0.94
alternate, H1: p>0.94
test statistic: 0.702
critical value: 1.645
decision: do not reject Ho
p-value: 0.2414
we do not have enough evidence to support the claim that The manufacturer of Nex claims that over 94% of patients taking Nex are cured in 8 weeks.