Please help me as soon as possible thx An article in fortune

An article in fortune (september 21, 1992)claimed that nearly one-half of all engineers continue academic studies beyond the B. S degree, ultimately receiving either an M. S degree. Data from an article in Engineering Horizons (Spring 1990) indicated that117 of 484 new engineering graduates were planning graduate study. Are the data from Engineering Horizons consistent with the claim reported by Fortune? Use a = 0. 09 in reaching your conclusions. Find the p- value. The true proportion of engineering students planning graduate studies significantly different from 0. 5 at a = 0. 09. The p-value is less than (choose the least possible).

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      
          
Using z table, we see that this z score is way off the table, so P must be very close to 0.

Thus, it is less than 0.001. [ANSWER]