Yes, good question. Always check conditions for any statistical method. This video just goes over the mechanics of using the calculator. For info on conditions for any of the methods in our calculator videos, check out our textbooks on openintro.org (there's a free PDF option).
If you mean, can you use a critical value (such as z* from the confidence interval calculation) to determine whether or not to reject the null hypothesis, the answer is "yes"! You can use the absolute value of "t" in the regression output (e.g. at 3:00) to compare against z* for a 2-sided test. One consideration for if you're in a course: some instructors may prefer one method over another.
Hi Zakiah, the p-value is all you need. Compare the p-value to your alpha. - If the p-value is smaller than alpha, reject H0. - If the p-value is larger than alpha, do not reject H0.