Hi,
I was asking myself the same thing. I stumbled upon a similar question to this one where they answered that they've used the socstatistics online P-Value calculator.

However, it was at a later lecture that I found out how to manually get the P-Value when using the T-Statistic. In order to get the P-Value, you would need to find the alpha that corresponds to the given T-Score on the table. In the case you're asking about, because the T-Score is 0.53 and the T-table provided does not have critical values lower than 1.282, we would have to use an online P-Value calculator or extrapolate.

Take the case of this lecture: https://learn.365datascience.com/courses/statistics/test-for-the-mean-dependent-samples

Here the degrees of freedom are 9 and the T-Score is 2.29. This is a value that, while not exactly on the table, it is between the values corresponding to alphas (levels of significance) of 0.025 and 0.01. Therefore, the P-Value must be a number between these two. We could use interpolation to get an approximation of this number or once again use an online P-Value calculator. I used both methods and ended up with the same result.

Hope this clarifies two things:

How they got the P-Value you're asking about
That the manual way of finding the P-Values differs when using a Z-Score/Table and a T-Score/Table

How did you get this P-Value

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