Question

Duck hunting in populated areas faces opposition on the basis of safety and environmental issues. In a survey to assess public opinion regarding duck hunting on Morro Bay (located along the central coast of California), a random sample of 750 local residents included 560 who strongly opposed hunting on the bay. Test the claim that more than 50% of local residents oppose hunting on Morro Bay. Use a significance level of 0.05.  USE PHANTOMS: Parameter, Hypotheses, Assumptions, Name, Test Test Statistic (round to 1 decimal places), Obtain the P-value, Make the Decision, Summary.

Answer 1

parameter : p

Ho :   p =    0.5                  
H1 :   p >   0.5       (Right tail test)          

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Assumptions:
sample size,n < 5% of population size,N
np>5 and n(1-p)>5
npq>10
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i proportion test

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Level of Significance,   α =    0.05                  
Number of Items of Interest,   x =   560                  
Sample Size,   n =    750                  
                          
Sample Proportion ,    p̂ = x/n =    0.7467                  
                          
Standard Error ,    SE = √( p(1-p)/n ) =    0.0183          

       
Z Test Statistic = ( p̂-p)/SE = (   0.7467   -   0.5   ) /   0.0183   =   13.5
                          
critical z value =        1.645   [Excel function =NORMSINV(α)              
                          
p-Value   = 0.00000 [Excel function =NORMSDIST(-z)      

      
Decision:   p-value<α , reject null hypothesis                       

There is enough evidence to say that more than 50% of local residents oppose hunting on Morro Bay.

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THANKS

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