Educators in a certain state claim that 70 of all high schoo

Educators in a certain state claim that 70% of all high school students in the state will attend college next fall. The principle at Beechnut High School claims that the proportion is much lower for his students. His school has an enrollment of 849 seniors, and 560 plan to attend college in the fall. At Alpha = 0.05, test the principle\'s claim.

Solution

2.

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   >=   0.7
Ha:   p   <   0.7

As we see, the hypothesized po =   0.7      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.659599529      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.015727359      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -2.568801981      
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    0.005102538      

significance level =    0.05      

As P < 0.05, we REJECT THE NULL HYPOTHESIS.      

Thus there is significant evidence that the proportion of high school students in the state that will attend college next fall is lower than the principle\'s claim. [CONCLUSION]