A new radar device is being considered for a certain missile

A new radar device is being considered for a certain missile defense system. The system is checked by experimenting with aircraft in which a kill or not kill is simulated. If, in 300 trials, 250 kills occur, accept or reject, at the 0.04 level of significance, the claim that the probability of a kill with the new system does not exceed the 0.8 probability of the existing device.

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   >=   0.8
Ha:   p   <   0.8
As we see, the hypothesized po =   0.8      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.833333333      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.023094011      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    1.443375673      
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    0.074457337      
significance level =    0.04      

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

Thus, at 0.05 level, there is no significant evidence that the new system does not exceed the 0.8 probability of the existing device. [ANSWER]