The director of admissions at a local college claims that 15

The director of admissions at a local college claims that 15% of students she interviews apply for admission. In a sample of 300 students, 30 applied for admission. At 0.05 significance evaluate the claim.

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.15
Ha:   p   =/=   0.15
As we see, the hypothesized po =   0.15      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.1      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.020615528      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -2.42535625      
          
As this is a    2   tailed test, then, getting the p value,  
          
p =    0.015293371      
significance level =    0.05      

Comparing p and the significance value, we   REJECT THE NULL HYPOTHESIS.      

There is significant evidence that the proportion of students she interviews that applies for admission is not 15%. [conclusion]