Suppose that against a certain opponent, the number of points the UCSB basketball team scores is normally distributed with an unknown mean θ and unknown variance σ^2. Suppose that over the course of the last 10 games between the two teams, UCSB scored the following points: 59, 62, 59, 74, 70, 61, 62, 66, 62, 75.
1. Compute a 95% t-confidence interval for θ. Does 95% confidence mean that the probability θ is in the interval you just found is 95%?
2. Now suppose that you learn that σ^2 = 25. Compute a 95% z-confidence interval for θ. How does this compare to the interval in the previous exercise?