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Hi Ruby,

The mistake you are making is that you are not using the t critical value like you are supposed to use. You are using the z critical value. In step 2 of the problem, you are going to the t table and looking up 0.005 in one tail (for 99% confidence), which is correct, but then you go straight to the bottom of the table to get the critical z value 2.576.

That is your error. Instead of going to the bottom of the t table, you should be stopping in the 28 degrees of freedom row because your sample size is only 29. Remember for 30 or less, we will use the t critical value with n - 1 degrees of freedom, not the z critical value which is found in the last row of the table. 

If you use the correct critical value, your margin of error will look like this:

2.763 * 4.25/SquareRoot(29) = 2.18057

Then you can add and subtract this margin of error to and from the mean to get the right interval.

Hope that makes sense,

Professor McGuckian