Standard deviation Vs. Standard error

Hi, for this question:
The value of a test statistic is best determined as the difference between the sample statistic and the value of the population parameter under H 0 divided by the: ?
The answer is the standard error of the sample statistic. Now I understand that we must use it when constructing confidence intervals aswell as when testing a distribution of means. But I can’t seem to grasp when we would use the standard deviation then? I thought when testing for a distribution we would use the standard deviation unless we were testing a distribution of sample means, so that is what I answered to this question.

Greetings friend! It looks like they are just asking for the definition of calculating the t-statistic here. They say “value” of the “test statistic” but they give you most of the t-statistic formula and want to know if you can spot the last part of it.

Please see generally

Fun fact - the term “t-statistic” is abbreviated from “hypothesis test statistic” and it is used in a t-test to decide whether to support or reject the null hypothesis. And low and behold, they in fact give you the null hypothesis (Ho) in your problem’s wording, so right there is perhaps a trigger/clue that it might be a t-test or t-statistic in the answer here.

And of course if others have better explanations I defer to them👍

Cheers - good luck - you got this👍