If we’re given an ANOVA table, and it asks for a prediction interval, should we use: mean +/- (given standard error)(t stat) or should we replace the given standard error with sqrt((standard error^2)((1 + (1/n) + ((x - mean)^2)/((n-1)(variance)))) I don’t understand when to use one or the other.

When n is too large you can use the given error value. If not, then unfortunately you’ll have to calculate the satndard error of the estimate using the formula you mentioned above.

Oh OK. Got it. Is there a magical “n” figure? 30? 100?

difference is prediction interval for a variable in the regression (which is the first equation) and 2nd equation is prediction interval for a forecast made using the regression.