A random sample of size n=16 is taken from a random variable X~N(mu, sigma), with variance unknown. The 95% confidence interval for mu (44.7, 49.9).
What are the values of the sample mean and the variance? (X bar and S)
I got X bar to be 47.3.
I then got: 44.7 = 47.3 - S/(sqrt 16)* t(15,.025) for S=20.4
Yes, you have gotten the mean right, it is the average of the end points.
$$\bar{x} - k S = 44.7$$
$$\bar{x} + k S = 44.7$$
where $k$ is known to you.
Since you already know $\bar{x}$, you can now solve for $\sigma$ in terms of $k$ and $\bar{x}$.