In One Sample Proportion test it is important to convert the

In One Sample Proportion test, it is important to convert the sample proportion to a z-score first. In this example, we selected a random sample of size 100 from a pool of university students and asked whether they use Facebook on a regular base. Sixty replied yes. Assuming that the population proportion under the null hypothesis is 50%, what is the z-score for the sample proportion?

1.50

1.75

2.00

2.25

Solution

Proportion ( P ) =0.5
Standard Deviation ( sd )= Sqrt (P*Q /n) = Sqrt(0.5*0.5/100)
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P(X = 0.6) = (0.6-0.5)/0.05
Z = 0.1/0.05= 2