A Government antipollution spokesperson asserts that more th

A Government antipollution spokesperson asserts that more than 80% of the plants in the Glassboro area meet the antipollution standards. An antipollution advocate does not believe the government claim. She takes a random sample of published data on pollution emission for 64 plants in the area and finds that 56 plants meet the pollution standards. Do the sample data support the government claim at the 5% level of significance? (Ho: =0.8; Ha: >0.8)

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 =    0.875      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.05      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    1.5      
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    0.066807201      
significance level =    0.05      

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

Thus, from this experiment, there is no significant evidence that more than 80% of the plants in the Glassboro area meet the antipollution standards. [CONCLUSION]