Extra Credit
You sell two types of chocolate, dark and light. You know that nationally more people buy light chocolate than dark, but you are wondering if this preference is stronger in one part of the county than another. You gather information on how many tons of chocolate were sold in the western, middle, and eastern parts of the country from the CCCCC (Cross Country Commission on Chocolate Consumption). Conduct a full hypothesis test using a chisquare (χ^{2}) test at the alpha (α) = .05 level.
Part of Country 

West 
Middle 
East 

Dark 
65 
72 
61 
Light 
91 
155 
145 
H_{o}: There is no relationship between chocolate preference and the part of the country where one lives.
H_{1}: There is a relationship between chocolate preference and the part of the country where one lives.
Alpha Level: Alpha (α) = .05
Rejection Rule: Reject H_{0} if chisquare computed (χ^{2}_{computed}) > 5.99. The degrees of freedom equals the number of columns of data minus 1 (3  1 = 2, in this case) times the number of rows of data minus 1 (2  1 = 1, in this case). Multiplying these (2 × 1) gives us 2 degrees of freedom. The general formula is written as (R  1) (C  1) = df. We then find the critical value in Table G on page 409, replicated, in part, below.
df 
5% 
1% 

1 
3.84 
6.64 

2 
5.99 
9.21 

3 
7.82 
11.34 

4 
9.49 
13.28 

5 
11.07 
15.09 

6 
12.59 
16.81 
Computation: First we total all rows and all columns.
Part of Country 

West 
Middle 
East 
Total 

Dark 
65 
72 
61 
198 
Light 
91 
155 
145 
391 
Total 
156 
227 
206 
589 
Then we do something that is really bizarre, we multiply the row total by the column total then divide this product by the grand total (589, in our case) to obtain an expected number for each cell.
Part of Country 

West 
Middle 
East 
Total 

Expect 
65 52.44143 
72 76.309 
61 69.24958 
198 
Expect 
91 103.5586 
155 150.691 
145 136.7504 
391 
Total 
156 
227 
206 
589 
Once you obtain the expected value (E) for each cell, you subtract the expected value from the observed value (O). You then square that difference for each cell. You then divide that squared difference by the expected value. You sum this last result for all of the cells and you have computed the ChiSquare.
O 
E 
O  E 
(O  E)^{2} 
(O  E)^{2}/E 
65 
52.441 
12.559 
157.7285 
3.007732 
72 
76.309 
4.309 
18.56748 
0.243320 
61 
69.25 
8.25 
68.0625 
0.982852 
91 
103.559 
12.559 
157.7285 
1.523078 
155 
150.691 
4.309 
18.56748 
0.123216 
145 
136.75 
8.25 
68.0625 
0.497715 
Total = Chi Square Computed = 
6.377439 
Decision: Reject H_{0}
Conclusion: There is a relationship between chocolate preference and the part of the country where one lives, χ^{2}(2, N = 589) = 6.377, p < .05.