It is believed that 36 of UNL students participate in intram

It is believed that 36% of UNL students participate in intramural sports. You think that the percentage is much higher than 36% since you and all of your friends play as many intramural sports as possible. You randomly sample 100 students and find that 30 of them play intramural sports. Perform a hypothesis test to test your claim. You must show all relevant steps and all of your work. (Notice that I did not specify a significance level) . Explain how the alternative hypothesis determines how to find the p-value.

Solution

Set Up Hypothesis
Under The Null Hypothesis H0:P>0.36
Under The Alternate Hypothesis H1: P<0.36
Test Statistic
No. Of Success chances Observed (x)=30
Number of objects in a sample provided(n)=100
No. Of Success Rate ( P )= x/n = 0.3
Success Probability   ( Po )=0.36
Failure Probability ( Qo) = 0.64
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.3-0.36/(Sqrt(0.2304)/100)
Zo =-1.25
| Zo | =1.25
Critical Value
The Value of |Z ?| at LOS 0.1% is 1.28
We got |Zo| =1.25 & | Z ? | =1.28
Make Decision
Hence Value of |Zo | < | Z ? | and Here we Do not Reject Ho
P-Value: Left Tail -Ha : ( P < -1.25 ) = 0.10565
Hence Value of P0.1 < 0.10565,Here We Do not Reject Ho

We have enough evidence that it is higher than 0.36