Consider the hypothesis test given by H o p 05 H 1 p 05

Consider the hypothesis test given by H o : p = 0.5 H 1 : p > .05 In a random sample of 100 subjects, the sample proportion is found to be p = 0.55. Is there sufficient evidence to justify the rejection of 0 H at the 0.01 level?

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 =    0.55      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.05      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    1      
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    0.158655254      
significance level =    0.01      

As P > 0.01, we   FAIL TO REJECT THE NULL HYPOTHESIS.  

Thus, there is no significant evidence that the true populaiton proportion is greater than 0.5. [CONCLUSION]