# The higher the IQ, the higher the average SATs results

Statistics Coursework

Hypotheses

1. The higher the IQ, the higher the average SATs results. There will be a stronger relationship between the girls’ IQ and SATs results than the boys’.

2. Boys will have a higher IQ than girls.

3. IQ will increase as age increases.

Plan

I have been given two sheets of containing 100 pieces of data on each. The data is secondary as I have not collected it myself. One set is from key stage three and the other from key stage four. The data includes year group, forename, age, gender, hair colour, eye colour, favourite type of music, IQ, height, weight, distance between home and school and SATs results.

I will use a sample of 80 students, because 200 is too time consuming. A sample of 80 will still give me a reliable answer. I will use a stratified sample so my sample is in proportion as the full set of data.

To do the stratified sample I am going to count how many year seven, eight, nine, ten and eleven students there are on the sheets of data. I will then divide the total number of year seven students by the total number of pupils, then times by 80. I will repeat this for the remaining year groups to complete my stratified sample.

Once I know the amount of students from all the different year groups I will use a calculator to generate random numbers for my data.

Hypothesis 1

The higher the IQ, the higher the average SATs results. There will be a stronger relationship between the girls’ IQ and average SATs results than the boys’.

To prove my first hypothesis I am going to plot IQ against the average SATs results on a scatter graph. I am doing this to see any correlation between the two. If my hypothesis is correct, I would expect a positive correlation.

To test the correlation I’m going to input the data into a graphical. I will then use it to calculate Pearsons’ Product Moment Correlation Coefficient. This will give me a value between -1 and 1, where -1 is a perfect negative correlation, 1 is a perfect positive correlation and values near o show no correlation. I would expect ...