In general, theories or hypotheses are set up for one or more objectives. Regards.

1. A t-test contains an implicit statistical hypothesis = that two sets of data come from the same normally-distributed population.

2. No, a single hypothesis can be used to test more than one research question.

Blaine Tomkins Thanks for your answer. But in my research, only one objective is comparing the results of two groups where I need to employ a t-test but the rest of the objectives are not about comparing any groups. So Can I develop a hypothesis only for one single objective where it is required or it will be methodologically incorrect? Kindly help me out

Aarti Singh You would only include a hypothesis when doing an inferential test, such as a t-test. If you're doing descriptive statistics with the data, such as only being interested in obtaining the mean, variance, standard deviation, percentiles, shape of the distribution, etc., - No, you do not need to include a hypothesis.

In short - Yes, you can create one hypothesis for the t-test and only look at descriptive statistics for the rest of the study. It's quite common to obtain both descriptive and inferential statistics in a study or project. It really comes down to what it is you want to know from the data.

Blaine Tomkins Thank you so much your answers and discussions always help to refresh thoughts.

Aarti Singh No problem. One last thing I should've mentioned above: when conducting a t-test, in most cases the researcher has a prediction about whether (or how) the two groups will differ, but no always. This has been referred to as a 'research hypothesis' by some.

If you're conducting a t-test simply to determine if two groups differ, but have no predictions about whether they differ or not - there is still a statistical hypothesis, but not a research hypothesis. In other words, there is always a statistical hypothesis when conducting an inferential test, but not necessarily always a research hypothesis.