To combat antibiotic resistance the Quality Improvement Cons

To combat antibiotic resistance, the Quality Improvement Consortium recommends a throat swab to confirm strep throat before a physician prescribes antibiotics to children under age 5. In a random sample of 83 children who received antibiotics for throat infections, 23 did not have a throat swab. At ? = 0.05, is this a statistically significant reduction over last year

Solution

Set Up Hypothesis
Under The Null Hypothesis H0:P=0.4
Under The Alternate Hypothesis H1: P<0.4
Test Statistic
No. Of Success chances Observed (x)=23
Number of objects in a sample provided(n)=83
No. Of Success Rate ( P )= x/n = 0.28
Success Probability   ( Po )=0.4
Failure Probability ( Qo) = 0.6
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.27711-0.4/(Sqrt(0.24)/83)
Zo =-2.29
| Zo | =2.29
Critical Value
The Value of |Z ?| at LOS 0.05% is 1.645
We got |Zo| =2.285 & | Z ? | =1.645
Make Decision
Hence Value of | Zo | > | Z ?| and Here we Reject Ho
P-Value: Left Tail -Ha : ( P < -2.28536 ) = 0.01115
Hence Value of P0.05 > 0.01115,Here we Reject Ho