Pearson chi-squared test (χ2): differences?

[Drudge]

So, as far as I know, there are two χ2-tests: "test for fit of a distribution" & "Test of independence"

How big of a mistake is it to use the one instead of the other in an exam for example (of course all exams are all different to some degree, but generally)?

The only differences I can really find out is how each test counts the theoretical value(s) and the way in which the degrees of freedom are counted

For example a problem might be as follows:
a random sample from population X is, as a function of age, distributed as follows

10-20
5
21-30
4
31-40
3
40-41
9

And the equivalent theoretical values are: 6, 5, 4, 5

Question:

"Does the sample represent the theoretical distribution?"

So, you would use a "test for fit of distribution", but how much of a difference is it to use a "test of independence"?

 

[Stephen Tashi]

So, you would use a "test for fit of distribution", but how much of a difference is it to use a "test of independence"?

That would depend on what theoretical distribution was stated in the problem.

 

[Drudge]

That would depend on what theoretical distribution was stated in the problem.

Non normal distribution.

 

[Stephen Tashi]

"Non-normal" is not a specific distribution. If you really want to know "how much" difference it would make you must be specific about the distribution - and if you are specific then you can calculate the difference yourself.