Hi!
I think I could help you! I did math studies, got a 19/20 on my IA. The title and the RQ were:
Investigation of the biological relationship between body length and shoe size in a group of women
RQ: Does a relationship between the two variables body length and shoe size in a group of women exist, or do they vary independently of each other?
I collected data from 386 women, it's a lot better to have an abundance of data than small samples of data. However my method was not random, as I explain and motivate in the section called Evaluation of methods used:
"Notice how the word “group” was included in the RQ;
Does a relationship between the two variables body length and shoe size in a group of women exist, or do they vary independently of each other?
This fact effectively conveys the message that it is not this investigation’s intention to discuss whether or not the results of this investigation can be applicable on the whole Swedish female population; the focus is primarily the group of 386 women in the group. Additionally, without the inclusion of the word “group” the method of the investigation would have had to be simple random sampling, a method which was consciously rejected as the method of sampling due to the amount of time that had to be spent in that case, due to the procedures of generating random numbers, assigning them to the subjects etcetera."
I did the following calculations:
1. Scatterplot
2. Correlation analysis including Pearson's product-moment correlation coefficient and the sample coefficient of determination
3. Regression analysis including least square regression line and the standard error of estimate
These calculations was then critically discussed (such as the fact that Pearson's tend to generate an incorrect picture of the strength of the relationship whilst the sample coefficient of determination doesn't).
I was much aided by the book
Hamburg, Morris. Basic Statistics: A Modern Approach (Third Edition). I used my GDC and the Minitab statistical package (free trial).
Hope that gave you an idea