I'm confused about the P-value

Hello,
Given that the T value is equal to 0.53, we can obtain the p-value from the t-distribution table considering n-1 degrees of freedom.
Best,
Ned

In the lesson the teacher say that formula 1- the number from the table, it uses with z-distribution table . is it use also with t-distribution table?

We use the n-1 degrees of freedom for T tests. A Z test does not use degrees of freedom. At which moment of the video is it said that a Z test used n-1 degrees of freedom, please?

T value is 0.53 and n-1 degrees is 9. But How the  p-value 0.304 is obtained ? I do not see how to get that value from the t table? it is 1 - something? Or just need to be calculated with the online tool

Manuel Carreno Yes , it was calculated through online calculator

There is still no information about how the p-score is calculated from the t-table. 

As far as I know, there are 2 ways of getting the p-value.

1. Using a p-value calculator. Go to https://www.socscistatistics.com/pvalues/ and choose, in this case, p-value from t score. You will need to input the T score (which is obtained from substracting the hypothesized mean to the sample mean, and then dividing by the standard error; 0.53), the degrees of freedom (sample size minus 1; 9), the significance level (0.05), and whether it is a one-sided or a two-sided test (one-sided in this case).

The result is p-value = 0.304. If the p-value is higher than the significance level (α), which in this case it is (0.304 > 0.05), the result is not significant, meaning we must accept the null hypothesis.

2. Using one of these Excel formulas: T.DIST ("returns the left-tailed Student's t-distribution"; I believe this means that H0 is less than or equal to some value), T.DIST.2T ("returns the two-tailed Student's t-distribution"; this would apply to the exercise of this lesson, where we are looking for a hypothesized mean of exactly 40%), or T.DIST.RT ("returns the right-tailed Student's T distribution"; this must apply when H0 is greater than or equal to some value).

The arguments for T.DIST are (x=[T-score value (use positive values preferrably, as the T.DIST.2T formula won't accept negative ones)], deg_freedom, cumulative = TRUE (don't understand the mechanics of this argument, but choosing FALSE will give us a value that differs from the calculator's, so better to stick to TRUE)).

Hope this helps. 

If you're wondering how to find the p-value of 0.304 manually (i.e. without Excel or a p-value calculator), you search for where the T-Score falls on the t-table on the row for the given degrees of freedom.

I'm not sure why how to do this manually isn't explained here since we received a whole lesson for how to do it with a z-table, but after some googling that is what I found. Similarly, the t-table in the video is only a portion of a more extended t-table. So, following the instructions above using the table in this video, you will not find the value you are looking for. Here is a more expanded table that helped me understand how 0.304 was obtained: https://t-tables.net/

So, in the case of the lesson (and using the table on the link above): 

- go to the row corresponding to 9 degrees of freedom

- find at which point (or between two values) we find our T-Score, |-0.53|. In our case, it falls between the first two values of 0.00 and 0.703

- from there, navigate to the top of the t-table where the significance levels are and find at which (or between which) significance level(s) your value/T-score is. Being this is a one-sided test, .53 falls between the 0.5 and 0.25 Significance levels. So, 0.304 makes sense. 

Obviously for simplicity's-sake and for the long term, it makes more sense to do this with the p-value calculator or with Excel, but if you're like me and appreciate knowing the how or why then I hope this explanation scratched that annoying itch to know.