Please help solve this A certain type of automobile is know

. A certain type of automobile is known to sustain no visible damage 25% of the time in 10-mph crash tests. A modified bumper design has been proposed to increase this percentage. Among 60 car crashes, 24 have no visible damage. Is the observed percentage increase real at the level of 5% or is it due to chance? State clearly your null and alternative hypothesis.

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   <=   0.25
Ha:   p   >   0.25

As we see, the hypothesized po =   0.25      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.4      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.055901699      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    2.683281573      
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    0.007290358      
significance level =    0.05      

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

Thus, there is significant evidence that the observed percentage increase is real. [CONCLUSION]