CAS Exam MAS-II Spring 2019, Question 11
Study guide: Exam MAS-II
Joe wants to use a Linear Mixed Model to determine if the use of any fertilizer results in a significantly different apple weight. After recording his observations for ten trees within the orchard, he has a dataset with the following form:
| Tree ID | Treatment | Apple Count | Trunk Diameter (cm) | Apple ID | Apple Weight (g) | Red Apple | Green Apple |
|---|---|---|---|---|---|---|---|
| 1 | Control | 20 | 14 | 1 | 83 | Y | N |
| 1 | Control | 20 | 14 | 2 | 65 | Y | N |
| 1 | Control | 20 | 14 | 3 | 76 | Y | N |
| 1 | Control | 20 | 14 | 4 | 69 | N | Y |
| 1 | Control | 20 | 14 | 5 | 87 | N | Y |
| … | … | … | … | … | … | … | … |
| 10 | Brand K | 18 | 18 | 178 | 94 | Y | N |
| 10 | Brand K | 18 | 18 | 179 | 102 | Y | N |
He has provided some notes to accompany his dataset:
- TREE ID and APPLE ID are both identifiers of the observation and therefore not considered to be covariates.
- The trees were either left untreated or treated with one of two brands (J or K).
- APPLE COUNT is the number of apples on a given tree.
- The apple can be only one of two colors: red or green.
You are given:
I. The apple dataset is an example of a two-level clustered dataset.
II. Including the Control Treatment in the intercept estimate and modeling Brand K and Brand J effect as the difference between the Control and the effect for Brand K or the difference between the intercept and Brand J will result in intrinsic aliasing.
III. If \beta_1 and \beta_2 represent the coefficients of the fixed effects associated with treatment, TREAT_J and TREAT_K, respectively, then the null and alternative hypotheses are as follows:
Null Hypothesis: $H_0: \beta_1 = 0$ and $\beta_2 = 0$
Alternative Hypothesis: $H_1: \beta_1 \neq 0$ or $\beta_2 \neq 0$
Determine which of the preceding statements are true.
- A) I only
- B) II only
- C) III only
- D) I, II and III
- E) The answer is not given by (A), (B), (C), or (D)
Answer this question and see the worked solution