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

question 16

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. $$\begin{array}{l}\begin{array} { c l c } \hline \text { Student } & \text { Gender } & \text { Score } \\\hline 1 & \text { Male } & 18 \\2 & \text { Female } & 17 \\3 & \text { Female } & 19 \\4 & \text { Female } & 16 \\5 & \text { Male } & 12 \\6 & \text { Female } & 15 \\7 & \text { Female } & 18 \\8 & \text { Male } & 16 \\9 & \text { Male } & 18 \\10 & \text { Female } & 20 \\\hline\end{array}\\\\\begin{array} { c l c } \hline \text { Student } & \text { Gender } & \text { Score } \\\hline 11 & \text { Female } & 17 \\12 & \text { Male } & 16 \\13 & \text { Male } & 16 \\14 & \text { Female } & 19 \\15 & \text { Female } & 16 \\16 & \text { Male } & 15 \\17 & \text { Female } & 12 \\18 & \text { Male } & 14 \\19 & \text { Female } & 16 \\20 & \text { Female } & 18 \\\hline\end{array}\end{array}$$ 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. Use α = .05. 12.8 Models with Both Quantitative and Qualitative Variables (Optional) 1 Write and Interpret Model with Quantitative and Qualitative Variables

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Definitions:

Dolls

Small, modeled figures representing humans or animals, used as toys for children or as collectibles for adults.

Stuffed Animals

Soft toys typically made from cloth and filled with a soft material, designed to resemble animals and often used as comfort objects by children.

Infants

Young children from birth to one year of age, an early stage of development focusing on rapid growth and learning.

Stopping Midair

The ability or action to bring a moving object or body to a halt while it is still suspended in the air.