Suppose I am given all of the necessary parameters about some linear model, but not the data itself. Namely, I am given $\hat{\beta}_1,\hat{\beta_0},\bar X, S_e, r^2$, etc. Also, I know that $X_1,\dots,X_n$ are all within the range of $[40,70]$. I'm being asked to construct a confidence interval for the expected difference in $Y$ over two units of $X$. What I'm not sure about is the parameter to be estimated.
I am guessing that a C.I. for $\mathbb{E}[Y|X=2]$ is not a good idea, because 2 is not within the range and the intercept will twist the results. I thought about estimating C.I. for $\mathbb{E}[Y|X=40+2]$ or $\mathbb{E}[Y|X=\bar{X}+2]$, the last one seems more reasonable but I can't think of any justification for it, let alone know whether this is the right approach at all.
Would appreciate any help.