How to Find RightTail Values and Confidence Intervals Using the tTable
You can use a ttable to find righttail probabilities and pvalues for hypothesis tests and to find t*values (critical values) for a confidence interval involving t. Unlike a Zdistribution, a tdistribution is not classified by its mean and standard deviation, but by the sample size of the data set being used (n). Unfortunately, there is no single “standard tdistribution” that you can use to transform the numbers and find probabilities on a table.
Because it wouldn’t be humanly possible to create a table of probabilities and corresponding tvalues for every possible tdistribution, statisticians created the ttable, which shows certain values of tdistributions for a selection of degrees of freedom and a selection of probabilities.
Each row of the ttable represents a different tdistribution, classified by its degrees of freedom (df). The columns represent various common greaterthan probabilities, such as 0.40, 0.25, 0.10, and 0.05. The numbers across a row indicate the values on the tdistribution (the tvalues) corresponding to the greaterthan probabilities shown at the top of the columns. Rows are arranged by degrees of freedom.
Another term for greaterthan probability is righttail probability, which indicates that such probabilities represent areas on the rightmost end (tail) of the tdistribution.
For example, the second row of the ttable is for the t_{2 }distribution (2 degrees of freedom, pronounced tee subtwo). You see that the second number, 0.816, is the value on the t_{2} distribution whose area to its right (its righttail probability) is 0.25 (see the heading for column 2). In other words, the probability that t_{2} is greater than 0.816 equals 0.25. In probability notation, that means p(t_{2 }> 0.816) = 0.25.
The next number in row two of the ttable is 1.886, which lies in the 0.10 column. This means the probability of being greater than 1.886 on the t_{2 }distribution is 0.10. Because 1.886 falls to the right of 0.816, its righttail probability is lower.
Follow these steps to use the ttable to find righttail probabilities and pvalues for hypothesis tests involving t:

Find the tvalue for which you want the righttail probability (call it t), and find the sample size (for example, n).

Find the row corresponding to the degrees of freedom (df) for your problem (for example, n – 1). Go across that row to find the two tvalues between which your t falls.
For example, if your t is 1.60 and your n is 7, you look in the row for df = 7 – 1 = 6. Across that row you find your t lies between tvalues 1.44 and 1.94.

Go to the top of the columns containing the two tvalues from Step 2.
The righttail (greaterthan) probability for your tvalue is somewhere between the two values at the top of these columns. For example, your t = 1.60 is between tvalues 1.44 and 1.94 (df = 6); so the right tail probability for your t is between 0.10 (column heading for t = 1.44) and 0.05 (column heading for t = 1.94).
The row near the bottom with Z in the df column gives righttail (greaterthan) probabilities from the Zdistribution.
Here’s how to use the ttable to find t*values (critical values) for a confidence interval involving t:

Determine the confidence level you need (as a percentage).

Determine the sample size (for example, n).

Look at the bottom row of the table where the percentages are shown.
Find your % confidence level there.

Intersect this column with the row representing your degrees of freedom (df).
This is the tvalue you need for your confidence interval.
For example, a 95% confidence interval with df = 6 has t * = 2.45. (Find 95% on the last line and go up to row 6.)