Question

Which statistical test should I use to assess if the duration of stay is different for those who received antibiotics versus those who did not?

Answer 1

That depends upon your sample sizes.

If your sample sizes are both less than 30, you can use t- test for independent samples

If your sample sizes are both 30 or more, you can use z- test for independent samples

In either case, you can use an α value of 0.05 and set up the following hypotheses:

Ho: μ (antibioitics) = μ (no antibiotics) versus Ha: μ (antibioitics) ≠ μ (no antibiotics)

If the p- value for your test is < 0.05, reject Ho else do not reject Ho.