CAS Exam MAS-II Fall 2018, Question 14
Study guide: Exam MAS-II
You are given the following information:
Ten classrooms are randomly assigned to receive one of three new teaching methods, labeled R, S and T. There are 300 students in these 10 classrooms. Student test scores are measured before and after the new teaching methods are implemented.
The following variables are considered:
- CLASS_ID — Class ID number
- METHOD_R — Indicator Variable (teaching method R = 1)
- METHOD_S — Indicator Variable (teaching method S = 1)
- STUDENT_ID — Student ID number
- SEX — Indicator variable (female = 1)
- SCORE_PRE — Student's test score before the new teaching method is implemented
- SCORE — Student's test score after the new teaching method is implemented
You are given Model 1 for the score of STUDENT_ID i in CLASS_ID j.
| Model | Model Specification |
|---|---|
| 1 | SCORE_{ij} = \beta_0 + \beta_1 \times SEX_{ij} + \beta_2 \times SCORE\_PRE_{ij} + \beta_3 \times METHOD\_R_j + \beta_4 \times METHOD\_S_j + u_j + \varepsilon_{ij} |
u_j \sim N(0, \sigma_{class}^2)\varepsilon_{ij} \sim N(0, \sigma^2)- All
u_j, \varepsilon_{ij}are mutually independent
Determine which of the following statements about Model 1 is true.
- A) There are seven parameters in the model.
- B) The value of
\beta_1varies across individual students. - C)
\sigma_{\text{class}}^2represents variance within the classroom. - D)
\sigma^2represents variance between the classrooms. - E) The intercept for each classroom is the same.
Answer this question and see the worked solution