A small mammal biologist is interested in whether there is a

A small mammal biologist is interested in whether there is an association between the incidence of rabies in raccoons and the area in which they are found. Two areas sampled, one on the east slope of the Cascades (E) and one on the west slope of the Cascades (W) Each raccoon observed was cross-classified according to which area it was seen and whether or not it had rabies. The observed frequencies are provided below: a) Write down null and alternative hypotheses for this study, either in words or mathematically. b) Calculate expected frequencies for each cell under the null table below. (5 pts) c) Using a chi-square test of independence to test the hypotheses in part (a), calculate the observed value of the test statistic. (5 pts) d) Write down the critical value for the statistical test, using a type I error rate of 0.05, and use it to make a decision regarding the null hypothesis. State a conclusion in the context of the original question.

Solution

A.

Ho: Rabies acquisition is independent of area.
Ha: Rabies acquisition is not independent of area.  
Doing an Expected Value Chart,          
          
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B.
Note that

Expecated value = row total * column total / overall total

Thus, these fill the table:

5.625   9.375
6.375   10.625

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c.

Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    3.020130719   [answer]  
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d.

With df = (a - 1)(b - 1), where a and b are the number of categories of each variable,          
          
a =    2      
b =    2      
          
df =    1      
          
Thus, the critical value is          
          
significance level =    0.05      
          
chi^2(critical) =    3.841458821   [ANSWER]

As chi^2 < chi^2 critical, we   FAIL TO REJECT THE NULL HYPOTHESIS.      
          
Thus, there is no significant evidence that the acquisition of rabies is not dependent of location. [conclusion]