Among drivers who have had car crashes in the last year 88 a

Among drivers who have had car crashes in the last year. 88 are randomly The results are listed below. Use a 5% significance level to set up a hypothesis test and test the claim car crashes occur uniformly over the four age groups. Show all work.

Solution

If the distribution is uniform, we expect 8/4 = 22 occurrences on each group.

Doing an observed/expected value table,          
O   E   (O - E)^2/E  
36   22   8.909090909  
21   22   0.045454545  
12   22   4.545454545  
19   22   0.409090909  
          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    13.90909091      
          
As df = a - 1,           
          
a =    4      
df = a - 1 =    3      
          
Then, the critical chi^2 value is          
          
significance level =    0.05      
chi^2(crit) =    7.814727903      
          
Also, the p value is          
          
p =    0.003031544      
          
Thus, comparing chi^2 and chi^2(crit) [or, p and significance level], we   REJECT THE NULL HYPOTHESIS.      
We conclude that there is significant evidence at 0.05 level that the distribution is NOT UNIFORM. [CONCLUSION]