Question

Consider a drug testing company that provides a test for marijuana usage. Among 326 tested​ subjects, results from 26 subjects were wrong​ (either a false positive or a false​ negative). Use a 0.10 significance level to test the claim that less than 10 percent of the test results are wrong.

Answer 1

Null hypothesis  
H0: P=0.10          
              
Alternative hypothesis  
H1: P < 0.10          
              
We have for given example,              
Population proportion value is =0.1          
x=26          
              
n=326          
Level of significance =   0.10          
Estimate for sample proportion = 0.0798          
              
Z test statistic formula for proportion

              
  
      
P-value=0.1115   .............................................by using Excel command =NORMSDIST(-1.22) or by using Z table.   
Decision:Do not reject   H0.      

Conclusion: We do not have sufficient evidence at 0.10 significance level to say that,  less than 10 percent of the test results are wrong.