The university registrar claims that fewer than 20 percent o

The university registrar claims that fewer than 20 percent of the students who enroll at Ivy University graduate in four years. To test this claim, a random sample of 100 students was selected and 18 were found to have graduated in four years. Calculate the p-value associated with the test statistic.

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   >=   0.2
Ha:   p   <   0.2
As we see, the hypothesized po =   0.2      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.18      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.04      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -0.5      
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    0.308537539   [ANSWER]