Suppose we would like to test the hypothesis that at least 1

Suppose we would like to test the hypothesis that at least 10% of students suffer from allergies. We collect a random sample of 225 students and 21 of them suffer from allergies.

State the null and alternative hypotheses.

Obtain a test statistic and a P-value.

State the conclusion at the =0.05 level.

Solution

Set Up Hypothesis
Null, at least 10% of students suffer from allergies H0:P>0.1
Alternate, not Ho, H1: P<0.1
Test Statistic
No. Of Success chances Observed (x)=21
Number of objects in a sample provided(n)=225
No. Of Success Rate ( P )= x/n = 0.0933
Success Probability ( Po )=0.1
Failure Probability ( Qo) = 0.9
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.09333-0.1/(Sqrt(0.09)/225)
Zo =-0.3333
| Zo | =0.3333
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =0.333 & | Z | =1.64
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Left Tail -Ha : ( P < -0.33333 ) = 0.36944
Hence Value of P0.05 < 0.36944,Here We Do not Reject Ho

We have evidence to indicate that at least 10% of students suffer from allergies