This is a homework question and I am want to make sure I am addressing this correctly. 1st that this is directional and my understanding of the null and alternative is correct. A researcher is...

This is a homework question and I am want to make sure I am addressing this correctly. 1st that this is directional and my understanding of the null and alternative is correct.

A researcher is interested in studying how working from home influences worker productivity. She compares the productivity of 30 workers in an office that is working remotely to the productivity of 30 workers in an office that is working in the office. She expects that the productivity of those working from home will be higher than those who are working in the office.
What is the null hypothesis and alternative for this scenario? Is it directional?

Null Hypothesis: productivity of 30 workers from home is less than and equal to the productivity of 30 workers at the office

Alternative: productivity of 30 workers from home is greater than the productivity of 30 workers at the office.