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

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 $$\text { Use } \alpha = .05$$