The actuarial student committee of a large firm has collected data on exam scores. A generalized linear model where the target is the exam score on a 0-10 scale is constructed using a log link, resulting in the following estimated coefficients

Predictor Variables	Coefficient
Intercept	– 0.1
Study Time (in units of 100 hours)	0.5
Attempt (1 for first attempt, else 0)	0.5
Master’s degree (1 for Yes, 0 for No)	– 0.1
Interaction of Attempt and Master’s degree	0.2

The company is about to offer a job to an applicant who has a Master’s degree and for whom the exam would be a first attempt. It would like to offer half of the study time that will result in an expected exam score of 6.0.

Calculate the amount of study time that the company should offer.

• 123 hours
• 126 hours
• 129 hours
• 132 hours
• 135 hours

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Key: C

Let [math]T[/math] be the study time offered. The equation to solve is

[[math]] \begin{aligned} 6.0 &= \exp[–0.1 + 0.5(2T) + 0.5 – 0.1 + 0.2] = \exp(0.5 + T) \\ 1.79176 &= 0.5 + T \\ T &= 1.29176 \end{aligned} [[/math]]

or 129 hours.

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.