Twenty Colleges Each Recommended One of Its Graduating Seniors for a Prestigious

question 64

Essay

Twenty colleges each recommended one of its graduating seniors for a prestigious graduate fellowship. The process to determine which student will receive the fellowship includes several interviews. The gender of each student and his or her score on the first interview are shown below.

$\begin{array}{clc}\hline \text { Student } & \text { Gender } & \text { Score } \\\hline 1 & \text { Male } & 18 \\2 & \text { Female } & 17 \\3 & \text { Female } & 19 \\4 & \text { Female } & 16 \\5 & \text { Male } & 12 \\6 & \text { Female } & 15 \\7 & \text { Female } & 18 \\8 & \text { Male } & 16 \\9 & \text { Male } & 18 \\10 & \text { Female } & 20\end{array}$

$\begin{array}{clc}\hline \text { Student } & \text { Gender } & \text { Score } \\\hline 11 & \text { Female } & 17 \\12 & \text { Male } & 16 \\13 & \text { Male } & 16 \\14 & \text { Female } & 19 \\15 & \text { Female } & 16 \\16 & \text { Male } & 15 \\17 & \text { Female } & 12 \\18 & \text { Male } & 14 \\19 & \text { Female } & 16 \\20 & \text { Female } & 18\end{array}$
a. Suppose you want to use gender to model the score on the interview y. Create the
appropriate number of dummy variables for gender and write the model.
b. Fit the model to the data.
c. Give the null hypothesis for testing whether gender is a useful predictor of the score y.
d. Conduct the test and give the appropriate conclusion $$\text { Use } \alpha = .05$$

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Definitions:

Income Statement

A financial statement that shows a company's revenues, expenses, and profits or losses over a specific time period.

Accounting Systems

The methods and processes utilized by an organization for tracking and managing its financial transactions, typically involving journals, ledgers, and financial statements.

Three-Step Process

A methodological approach that divides a task or problem into three distinct phases for easier management and resolution.

Analysis

The process of examining components or data sets to understand their structure, relationships, and implications.