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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.

H_o: 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 (χ²_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.

Computation: First we total all rows and all columns.

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.

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.

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.

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