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 chi-square (χ2) test at the alpha (α) = .05 level.

 Part of Country West Middle East Dark 65 72 61 Light 91 155 145

Ho: There is no relationship between chocolate preference and the part of the country where one lives.

H1: There is a relationship between chocolate preference and the part of the country where one lives.

Alpha Level: Alpha (α) = .05

Rejection Rule: Reject H0 if chi-square computed (χ2computed) > 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 Dark  Expect 65 52.44143 72 76.309 61 69.24958 198 Light  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 Chi-Square.

 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 H0

Conclusion: There is a relationship between chocolate preference and the part of the country where one lives, χ2(2, N = 589) = 6.377, p < .05.