Hypothesis testing - Don't know what hypotheses to use.

[Ethan3141]

I don't know which Hypotheses to use, here are the ones I considered:

• [MATH]H_0:\mu_A=\mu_B, H_1:\mu_A\neq\mu_B[/MATH] The issue I have with this is [MATH]n_A,n_B<30[/MATH] which means I have to use the t-distribution but then the degrees of freedom is calculated by [MATH]n_A+n_B-2=20+20-2=38[/MATH] and the table only goes up to 30.
• [MATH]H_0:\mu_d=0, H_1:\mu_d\neq0[/MATH] The issue I have with this is it means the data has to be paired which I am not sure if it is or not, the fact that [MATH]n_A=n_B[/MATH] is the only thing making me think it could be paired but I am sure this is not a definite indicator. Also I think [MATH]\mu_d=\mu_A-\mu_B[/MATH] is true but I am not sure.

In short I just don't know what my hypotheses should be and if the data is paired or independent/how to determine this (it probably requires common sense which I lack). Any help will be greatly appreciated.

Disclaimer: I have a similar titled post; these two posts are different questions. I am limiting myself to a max of two questions per day as to not abuse the service (If this is too many please let me know).

Thanks, Ethan