The Data Below Represents the Fields of Specialization for a Randomly

Essay

The data below represents the fields of specialization for a randomly selected sample of undergraduate students. We want to determine whether there is a significant difference in the fields of specialization between regions of the country.
$$\begin{array} { l r r r r r } & \text { Northeast } & \text { Midwest } & \text { South } & \text { West } & \text { Total } \\\text { Business } & 54 & 65 & 28 & 93 & 240 \\\text { Engineering } & 15 & 24 & 8 & 33 & 80 \\\text { Liberal Arts } & 65 & 84 & 33 & 98 & 280 \\\text { Fine Arts } & 13 & 15 & 7 & 25 & 60 \\\text { Health Sciences } &\underline{ 3}& \underline { 12 } & \underline { 4 } & \underline { 21 } & \underline { 40 } \\&150&200&80&270&700\end{array}$$
a. Determine the critical value of the chi-square ?2 for this test of independence.
b. Calculate the value of the test statistic.
c. What is the conclusion for this test? Let ? = .05.