The manufacturer of a spot remover claims that has product r

The manufacturer of a spot remover claims that has product removes 90 percent of all spots. If, in a random sample, only 174 of 200 spots were removed with the manufacturer\'s product, test the null hypothesis theta = 0.90 against the alternative hypothesis theta

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   >=   0.9
Ha:   p   <   0.9
As we see, the hypothesized po =   0.9      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.87      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.021213203      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -1.414213562      
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    0.078649604      

significance level =    0.05      

As P > 0.05, we   FAIL TO REJECT THE NULL HYPOTHESIS.      

Thus, there is no significant evidence that the product does not remove more than 90% of all spots. [CONCLUSION]