Question

In a simple random sample of 70 automobiles registered in a certain state, 26 of them were found to have emission levels that exceed a state standard. Can it be concluded that less than half of the automobiles in the state have pollution levels that exceed the standard? Find the P-value and state a conclusion. Round the answer to four decimal places.

- The P-value is : _____

- We can conclude that less than half of the automobiles in the state have pollution levels that exceed the standard.

Answer 1

Ho :   p =    0.5                  
H1 :   p <   0.5       (Left tail test)          
                          
Level of Significance,   α =    0.05                  
Number of Items of Interest,   x =   26                  
Sample Size,   n =    70                  
                          
Sample Proportion ,    p̂ = x/n =    0.3714                  
                          
Standard Error ,    SE = √( p(1-p)/n ) =    0.0598                  
Z Test Statistic = ( p̂-p)/SE = (   0.3714   -   0.5   ) /   0.0598   =   -2.1514
                          

                          
p-Value   =   0.0157   [excel function =NORMSDIST(z)]              
Decision:   p-value<α , reject null hypothesis                       
                      
There is enough evidence that less than half of the automobiles in the state have pollution levels that exceed the standard.

                       

Please revert back in case of any doubt.

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