A random sample of $50$ men shows the following relation between annual income $Y$ (in dollars) and education $X$ (in years): estimator for $Y, (\hat{Y}) = 1200 + 800X $
Average income is $Y = \$10,000$ and average education is $X = 11.0$ years.
The variance is $900$ and the residual standard deviation about the fitted line is $s = \$7300$.
I need to make a $95\%$ interval for the population slope, but am unsure of which value to use for $X$, the sample mean. I have the mean for both of my variables, but how do I know which one to use? Any help is appreciated as I'm new at this and trying to get ahead on some concepts.
You don't calculate the CI for a regression slope using any particular X value. You use all the data. The link here has the actual formula for calculating the CI under the typical normal assumptions. In general, you need to become comfortable with T-statistics in order to do standard inference with simple linear regression.