A school teacher has two different exercises (exercise 1 and exercise 2) that he
ID: 3066744 • Letter: A
Question
A school teacher has two different exercises (exercise 1 and exercise 2) that he believes help students to remember what is taught in a class. Both exercises involve an interactive five-minute activity that students can complete at the beginning of a class. The teacher would like to study the effect of each exercise and the interaction of these effects.
The teacher gathers four simple random samples of school students and treats them to the two different exercises. One sample receives neither exercise, one sample receives exercise 1, one sample receives exercise 2, and one sample receives both exercises. A memory test is given at the end of the lesson to measure the amount of the lesson they remember.
A two-way ANOVA test is conducted by the teacher, to determine the significance of the effect of each exercise, and the interaction of the two exercises. A level of significance of 0.05 is used.
An output table for this test and a means plot for the samples collected are included below:
a)Based on the output table for the ANOVA test:
it can be concluded that there is no interaction between exercise 1 and exercise 2 in relation to their effect on memory
it can be concluded that there is interaction between exercise 1 and exercise 2 in relation to their effect on memory
there is not enough evidence to make a conclusion about the interaction of exercise 1 and exercise 2 in relation to their effect on memory
b)Four colleagues of the teacher look at the means plot and each colleague makes a comment about it:
Doctor Drake: 'It appears that if a student completes both exercises, their memory capacity is roughly the same as if the student completed either one of the exercises in isolation. That is, doing one of the exercises will help the memory capacity but then also doing the other exercise will not help memory capacity further.'
Professor Patterson: 'It appears that if a student completes both exercises, their memory capacity increases by more than the sum of the increases caused by each exercise in isolation. That is, each exercise tends to enhance the effect of the other.'
Headmaster Harry: 'It appears that if a student completes both exercises, their memory capacity is greatly decreased compared to when the student completes either one of the exercises in isolation. That is, each exercise tends to negate the effect of the other.'
Instructor Ian: 'It appears that the completion of one of the exercises has no impact on the effect of completing the other exercise. So the effect of completing the two exercises on memory capacity is roughly the sum of the effects of completing each exercise in isolation.'
The colleague that most accurately describes the relationship suggested by the means plot is:
Doctor Drake
Professor Patterson
Headmaster Harry
Instructor Ian
Explanation / Answer
a)Based on the output table for the ANOVA test:
As, the p-value of Interaction is 0.0178, which is less than significance level (0.05),
it can be concluded that there is interaction between exercise 1 and exercise 2 in relation to their effect on memory
b)Four colleagues of the teacher look at the means plot and each colleague makes a comment about it:
The pink line with the square box (Excercise 2 = Yes) is parallel to the x-axis. This shows that if Exercise 2 is done, the memory capacity is same whether Exercise 1 is Yes or No. So, if if Exercise 2 is done, there is no improvement in memory capacity whether Exercise 1 is done or not.
Similarly for (Excercise 1 = Yes), the memory capacity is same whether Exercise 2 is Yes or No. (See both the lines in the plot, meets at the point where Excercise 1 = Yes). This shows that if Exercise 1 is done, the memory capacity is same whether Exercise 2 is Yes or No. So, if if Exercise 1 is done, there is no improvement in memory capacity whether Exercise 2 is done or not.
So, the correct option is Doctor Drake.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.