A researcher wanted to determine whether certain accidents were uniformly distri

Question

A researcher wanted to determine whether certain accidents were uniformly distributed over the days of the week. The data show the day of the week for n = 299 randomly selected accidents. Is there reason to believe that the accident occurs with equal frequency with respect to the day of the week at the alpha = 0.05 level of significance? Click the icon to view the table. H_1: At least one proportion is different from the others. Compute the expected counts for day of the week. What is the test statistic? chi^2_0 = (Round to three decimal places as needed.)

Explanation / Answer

Doing an observed/expected value table,          
O   E   (O - E)^2/E  
37   42.71428571   0.764452938  
39   42.71428571   0.322981366  
26   42.71428571   6.540372671  
40   42.71428571   0.172479694  
42   42.71428571   0.011944577  
52   42.71428571   2.01863354  
63   42.71428571   9.634018156  
          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    19.46488294   [ANSWER, TEST STATISTIC]

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Other information:  
          
As df = a - 1,           
          
a =    7      
df = a - 1 =    6      
          
Then, the critical chi^2 value is          
          
significance level =    0.05      
chi^2(crit) =    12.59158724      
          
Also, the p value is          
          
p =    0.003446478      
          
Thus, comparing chi^2 and chi^2(crit) [or, p and significance level], we   REJECT THE NULL HYPOTHESIS.      
          

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