The null hypothesis is that the true proportion of the popul

The null hypothesis is that the true proportion of the population is equal to .40. A sample of 120 observations revealed the the sample proportion \"p\" was equal to .30. At at the .05 significance level test to see if the true proportion is in fact different from .40. Did you reject the null hypothesis?

Solution

Set Up Hypothesis
Null, H0:P=0.4
Alternate, H1: P!=0.4
Test Statistic
No. Of Success chances Observed (x)=36
Number of objects in a sample provided(n)=120
No. Of Success Rate ( P )= x/n = 0.3
Success Probability ( Po )=0.4
Failure Probability ( Qo) = 0.6
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.3-0.4/(Sqrt(0.24)/120)
Zo =-2.2361
| Zo | =2.2361
Critical Value
The Value of |Z | at LOS 0.05% is 1.96
We got |Zo| =2.236 & | Z | =1.96
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != -2.23607 ) = 0.02535
Hence Value of P0.05 > 0.0253,Here we Reject Ho

We have evidence that true proportion is in fact different from .40