The Data Below Represents the Fields of Specialization for a Randomly

question 19

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.

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Definitions:

Income

The monetary return or earnings received by an individual or entity, often measured on a regular basis, such as monthly or annually.

Consumption Bundle

A combination of goods and services that a consumer chooses to consume given their budget constraints.

Utility Function

A mathematical representation of how consumers rank different bundles of goods according to their level of satisfaction or utility.

Consumption

The process by which goods and services are used up by consumers.