Question: Aspen Trees: Base Circumference In Roosevelt Nat’l Forest, the took random samples of live aspen trees and measured the base circumference of each tree.

1. The first sample had 30 trees with a mean circumference of \(\bar{X}\) = 15.71 in. and a sample standard deviation of \(\sigma \) = 4.63 in. Find a 95% confidence interval for the mean circumference of aspen trees from these data.
2. The next sample had 90 trees with a mean of \(\bar{X}\) = 15.58 in. and a sample standard deviation of \(\sigma \) = 4.61 in. Again, find a 95% confidence interval from these data.
3. The last sample had 300 trees with a mean of \(\bar{X}\) =15.59 in. and a sample standard deviation of \(\sigma \) = 4.62in. Again, find a 95% confidence interval from these data.
4. Find the length of each interval of parts (a), (b), and (c). Comment on how these lengths change as the sample size increases.

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