Question

he mayor of a town has proposed a plan for the construction of an adjoining bridge. A political study took a sample of 1000 voters in the town and found that 57% of the residents favored construction. Using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is above 53%. Make the decision to reject or fail to reject the null hypothesis at the 0.20 level.

Answer 1

Ho :   p =    0.53                  
H1 :   p >   0.53       (Right tail test)          
                          
Level of Significance,   α =    0.20                  
Number of Items of Interest,   x =   570                  
Sample Size,   n =    1000                  
                          
Sample Proportion ,    p̂ = x/n =    0.5700                  
                          
Standard Error ,    SE = √( p(1-p)/n ) =    0.0158                  
Z Test Statistic = ( p̂-p)/SE = (   0.5700   -   0.53   ) /   0.0158   =   2.5344
                          
  
p-Value   =   0.0056 [Excel function =NORMSDIST(-z)              
Decision:   p-value<α =0.20 , reject null hypothesis                       
There is enough evidence to support the claim that     the percentage of residents who favor construction is above 53%