A new drug, Broctin, is administered to 100 patients with a particular disease.

Question

A new drug, Broctin, is administered to 100 patients with a particular disease. 50 of these individuals improve after taking Broctin. Another drug, Statisticin, has been in use for some time and is known to produce improvement in 45% of administered patients with the same disease. A pharmaceutical company wants to know whether Broctin leads to a significant increase in the number of individuals that improve from the disease when compared to Statisticin.

Please carry out the appropriate analysis and report your calculated z-score. Please round your answer to three decimal places.

Explanation / Answer

Set Up Hypothesis
Null, H0:P<0.45
Alternate, H1: P>0.45
Test Statistic
No. Of Success chances Observed (x)=50
Number of objects in a sample provided(n)=100
No. Of Success Rate ( P )= x/n = 0.5
Success Probability ( Po )=0.45
Failure Probability ( Qo) = 0.55
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.5-0.45/(Sqrt(0.2475)/100)
Zo =1.005
| Zo | =1.005
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =1.005 & | Z | =1.64
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Right Tail - Ha : ( P > 1.00504 ) = 0.15744
Hence Value of P0.05 < 0.15744,Here We Do not Reject Ho

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