A local zoo is interested in knowing if age is a factor when choosing to the ent

Question

A local zoo is interested in knowing if age is a factor when choosing to the enter the aquarium. As patrons enter the zoo, a random sample are asked their age and whether or not they intend to visit the aquarium. Data is shown in the table below; please perform a test to determine if age makes a difference in their choice to enter the aquarium. Be sure to give an interpretation with your answer.

Ages Enter Aquarium Not Enter Total 18> 53 27 80 18-40 72 58 130 40< 61 29 90 Total 186 114 300

Explanation / Answer

Let the test be at 0.05 level.

Doing an Expected Value Chart,          
          
49.6   30.4  
80.6   49.4  
55.8   34.2  
          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    4.30334262      
          
With df = (a - 1)(b - 1), where a and b are the number of categories of each variable,          
          
a =    2      
b =    3      
          
df =    2      
          
Thus, the critical value is          
          
significance level =    0.05      
          
chi^2(critical) =    5.991464547      
          
Also, the p value is          
          
P =    0.116289639      
          
As chi^2 < 5.991, and P > 0.05, we   FAIL TO REJECT THE NULL HYPOTHESIS.      
          
Thus, there is no significant evidence that age makes a difference in their choice to enter the aquarium at 0.05 level. [CONCLUSION]  

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