In a study of vehicle ownership, it has been found that 22.4% of U.S. households

Question

In a study of vehicle ownership, it has been found that 22.4% of U.S. households do not own a vehicle, with 42.3% owning 1 vehicle, and the remaining owning 2 or more vehicles. The data for a random sample of 150 households in a resort community are as follows: 46 owned 0 vehicles, 68 owned 1 vehicle, and the remaining owned 2 vehicles. When testing (at the 5% level of significance) whether the vehicle-ownership distribution in this community differs from that of the nation as a whole what is the null and alternative hypotheses? (please write out the null and alternative hypotheses below AND on your scratch work...failure to do BOTH will result in 0 points)

Explanation / Answer

Here,

Ho: The vehicle-ownership distribution in this community does not differ from that of the nation as a whole.

Ha: The vehicle-ownership distribution in this community differs from that of the nation as a whole.

Doing an observed/expected value table,          

          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    10.32839169      
          
As df = a - 1,           
          
a =    3      
df = a - 1 =    2      
          
Then, the critical chi^2 value is          
          
significance level =    0.05      
chi^2(crit) =    5.991464547      
          
Also, the p value is          
          
p =    0.005717659      
          
Thus, as chi^2 > 5.991, and P < 0.05, we   REJECT THE NULL HYPOTHESIS.      
          
Thus, there is significant evidence that the vehicle-ownership distribution in this community differs from that of the nation as a whole at 0.05 level. [CONCLUSION]

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