## My Hypothesis

I will now use raw data from my school (the Swaminarayan School). Then I will make a hypothesis, which I will then try to prove. My hypothesis is too seeing whether there is correlation between the maths scores and the CAT scores.

I have decided that I will be using a sample size of 30 as less than 30 would not represent the population. More than 30 would make it rather difficult to plot the data on the scatter graph. I will be doing a stratified random sample so that when I standardise the data it will correspond with the proportion of data sets.

When a student is scheduled to join our school he/she will take an IQ (CAT) test. So, I will not have to arrange for an IQ test to take place.

There are five different tables.

Table 1 consists of 11 students.

Table 2 consists of 9 students.

Table 3 consists of 22 students.

Table 4 consists of 18 students.

Table 5 consists of 23 students.

This leads to a total of 83.

I will now determine how many students I have to use from each table.

This is determined by:-

Num of Students in Table * by Num of data I’m using = Num of data I

Total Number of Students has to use.

Table 1=11/83*30=3.97 rounded up to 4.

So this means I will use 4 students from table 1.

Table 2=9/83*30=3.25 rounded down to 3.

So this means I will use 3 students from table 2.

Table 3=22/83*30=7.95 rounded up to 8.

So this means I will use 8 students from table 3.

Table 4=18/83*30=6.5 rounded up to 7.

So this means I will use 7 students from table 4.

Table 5=23/83*30=8.31 rounded down to 8.

So this means I will use 8 students from table 5.

I will now have to determine a way of randomising the results to keep it fair. There are two methods of which I can do this. The first method is to use the randomising button on the scientific calculator. Or my other option is to pick it out of a hat. I have selected the randomising button on my calculator as it is the easier, faster and more efficient way of selecting random numbers.

Randomly Selected Students.

From Table 1:

- 2
- 8
- 6
- 11

From Table 2:

- 4
- 5
- 9

From Table 3:

- 6
- 10
- 2
- 20
- 8
- 22
- 17
- 5

From table 4:

- 16
- 5
- 6
- 10
- 4
- 14
- 9

From Table 5:

- 6
- 21
- 14
- 7
- 17
- 12
- 11
- 4

Proving My Hypothesis.

Because everything has been decided I shall now make a scatter graph to prove my hypothesis. I will distinguish whether there is a correlation and then use the Spearman’s Rho Theorem to learn the strength of the correlation.

As seen above there is positive correlation between the Maths results and the CAT results.

I will know learn the strength of the two positive by using the Spearman’s Rho Theorem.

Spearman’s Rho Theorem

I will be explaining the method in steps to ensure clarity.

Step One.

In order to do this I have included a table underneath. A key is included.

Step 2

My Sample Size will now have to be stated. I will refer to it as N.

Step 3

I will now have to count the number of paired scores. In this case the number of paired scores is 30. So N=30.

Step 4

I will now multiply N by it’s own value, twice, then subtract it’s own value.

(30*30*30)-30 =27000-30=26970.

Step 5

I shall now total all the values in the column D2.

49+110.25+1+20.25+12.25+0.25+4+42.25+6.25+6.25+64+1+100+30.25+272.25+49+1+1+625+1+0+2.25+36+81+16+81+225+20.25=

1872.25

Step 6

I will now multiply the value I obtained in step 5 by 6; then divide the result by the value I found in step 4.

1872.25*6 = 11233.5 =0.4165 to four d.p

26970 26970

Step 7

I shall now find Rho by subtracting the number I obtained in step 6 from 1.

1-0.4165=0.5835

Step 8

My Rho number has exceeded all of the numbers below:

0.306

0.364

0.432

0.478

My Conclusion

I am going to end my coursework by expressing how I would improve on my hypothesis should the opportunity to repeat it arise. I may use a bigger population or maybe use different methods to randomize numbers. I am glad that my hypothesis didn’t turn out to be a null one. From this investigation I have learnt a lot about statistics and would jump at the opportunity to learn more about the topic.