May I please get some help with this question Please explain

May I please get some help with this question? Please explain so I can learn how to solve this.

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.5
Ha:   p   =/=   0.5
As we see, the hypothesized po =   0.5      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.241735537      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.022727273      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -11.36363636      
          
As this is a    2   tailed test, then, getting the p value,  
          
p =    6.34475*10^-30      

significance level =    0.08      

Comparing as P < 0.08, we   REJECT THE NULL HYPOTHESIS.      
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Thus, the true proportion of engineering students planning graduate studies IS significantly different from 0.05 at a = 0.08.

The P value is less than 0.001. [ANSWER]