In a recent study researchers found that 47 out of 300 boys

In a recent study, researchers found that 47 out of 300 boys aged 7-13 were overweight or obese. On the basis of this study can we conclude that more than 15% of the boys aged 7-13 in the sampled population are overweight or obese? Use a 5% level of significance. Give the null and alternative hypotheses, calculate the test statistic (show your work), and give your conclusion including a comparison to alpha or the critical value to receive full credit.

Solution

Set Up Hypothesis
Null, no evidence to support the cliam H0:P=0.15
Alternate, more than 15% of the boys are over weighted H1: P>0.15
Test Statistic
No. Of Success chances Observed (x)=47
Number of objects in a sample provided(n)=300
No. Of Success Rate ( P )= x/n = 0.1567
Success Probability ( Po )=0.15
Failure Probability ( Qo) = 0.85
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.15667-0.15/(Sqrt(0.1275)/300)
Zo =0.3234
| Zo | =0.3234
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =0.323 & | Z | =1.64
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Right Tail - Ha : ( P > 0.32338 ) = 0.3732
Hence Value of P0.05 < 0.3732,Here We Do not Reject Ho

We conclude that we have no evvidence to support more than 15% of the boys are over weighted