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Hi Cristina,

This problem is very likely to be on the exam. Whenever your degrees of freedom are not on the t-table, we take the nearest answer that has degrees of freedom below the value we need.

For example, if your alpha/2 is 0.025 and you want the critical t value that has 52 degrees of freedom, you will look up 0.025 under 50 degrees of freedom because 50 is the closest available value that is less than 52. Notice that even if we needed 0.025 with 54 degrees of freedom, we would choose the 0.025 and 50 degrees of freedom because we want the closest value to our desired degrees of freedom that is less than the value we need. This will ensure we are being conservative by providing a confidence level that is slightly higher than specified in the problem.  This is true because the values with smaller degrees of freedom are always larger. These values make our interval wider, which increases our confidence level. Of course, if the exact degrees of freedom is on the table, we will always take the exact value, but when it isn't there we make the conservative choice.

Hope that makes sense; if not, it is covered in this video at about the 2:40 mark: http://www.statsprofessor.com/video.php?chapterId=16&id=309#ptop

Professor McGuckian