Hypothesis testing!!

Question

I am so lost in where to begin for this question...

 

A random sample of 10 students were trying to determine which profession was best suites for them. They each took aptitude tests for Social Work and Law. The SW test yielded ordinal level scores ranging from 1-10. The Law test involved a 20 item multiple choice test. is there an association between aptitude for SW and aptitude for Law in this sample? does the association exist in the population from which the sample was drawn?

 

Student    Social work aptitude score       Number of correct scores on Law test

a                         10                                               7

b                          6                                                8

c                          1                                                17

d                          8                                                10

e                          3                                                13

f                           8                                                 9

g                          2                                                20

h                          5                                                 8

i                           8                                                 6

j                           4                                                18

 

Answer 1

There's an obvious negative association -- it jumps right out at you if you simply graph the scores on a scatter plot treating the social work aptitude score as the independent variable X, and the law test score as the dependent variable Y (you can do that in Excel without needing to resort to any more specialized software).

 

To know how you're supposed to solve the problem, though, I'd need to know more about the class you're taking and what subject matter you're covering.  The strength of the association would probably be measured using Pearson's correlation coefficient; to determine whether the association is likely to exist in the population from which the sample was drawn, you would probably calculate the Fisher transformation of that correlation coefficient.

 

Actually doing those calculations would take more time than I have right now (and might create an academic honesty issue as well), and if those terms don't sound familiar from the course you're taking then that's probably not what you're supposed to do anyway.  You could also use simple linear regression to identify the association between the two sets, but I don't think that leaves you with a good way of testing whether the association exists in the population.