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:

Peekaboo

A game played with babies that involves hiding and suddenly reappearing, intended to entertain and develop the child's understanding of object permanence.

Object Permanence

The understanding that objects continue to exist even when they cannot be seen, heard, or otherwise sensed, a concept developed during infancy.

Love

A complex set of emotions and attitudes associated with strong feelings of affection, warmth, and respect for another person.

Gender Development

The process by which individuals develop their gender identity, often influenced by biological, social, and cultural factors.