A Statistics Course Coordinator Is Trying to Improve the Teaching

Essay

A statistics course coordinator is trying to improve the teaching quality of her course.
Last semester, her class list was randomly divided into three separate groups, A, B and
C.
Group A are offered two, one hour lectures per week and one, one-hour tutorial per week, where the maximum number in a tutorial class is 10, and their continuous assessment is individual based.
Group B are offered two one hour lectures per week and one two hour tutorial per week where the average tutorial class size is 42 and the continuous assessment is team based, where students are randomly allocated to a team of 7 students each in their tutorial class.
Group C have one four hour lecture including combined tutorial per week and their continuous assessment is individual based, where this class size is 50 students.
A random sample of students from each of group A, B and C was selected with their final marks given in the following table: $$\begin{array} { | c | c | c | } \hline \text { Group A } & \text { Group B } & \text { Group C } \\\hline 75 & 50 & 50 \\\hline 68 & 63 & 65 \\\hline 99 & 45 & 81 \\\hline 72 & 55 & 58 \\\hline 52 & 75 & 75 \\\hline\end{array}$$
a. Is there significant evidence at the 10% level of significance for the course coordinator to infer that there exists a difference in the population mean final mark of the three different teaching methods?
b. What assumption about the distribution of final grades was needed in order to carry out the F-test of the analysis of variance?