A local private school has a statement in their recruiting m

A local private school has a statement in their recruiting materials that says no more than 35% of the students commute more than14 miles one way to school. In a sample of 35 students, 16 indicate they drive more than 14 miles one way. Test the null hypothesis at the a= 0.05 level. (Assume the variable is approximately normally distributed.)

need step by step

Solution

Set Up Hypothesis
Null, H0:P<=0.35
Alternate, H1: P>0.35
Test Statistic
No. Of Success chances Observed (x)=16
Number of objects in a sample provided(n)=35
No. Of Success Rate ( P )= x/n = 0.4571
Success Probability ( Po )=0.35
Failure Probability ( Qo) = 0.65
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.45714-0.35/(Sqrt(0.2275)/35)
Zo =1.3289
| Zo | =1.3289
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =1.329 & | Z | =1.64
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Right Tail - Ha : ( P > 1.32894 ) = 0.09193
Hence Value of P0.05 < 0.09193,Here We Do not Reject Ho

in their recruiting materials that says no more than 35% of the students commute
more than 14 miles one way to school.