Does the Central Limit Theorem require the number of random variables to increase to a sufficiently large number or the number of samples of each random variable to increase to a sufficiently large number?
If the number of random variables is 1 for the chi-square statistic (as an example), then the degrees of freedom is 1, and the distribution would not represent a normal distribution, no matter how many samples. However, if the number of random variables is large, it seems we would still require more than a few samples for the chi-square distribution to resemble a normal distribution.
Note: I am starting to self learn statistics, and may need some contextual info in answers.