Answer
We can say with 95% confidence that the mean diameter of a Douglas fir tree in the western Washington Cascades is between 129.01 and 165.59 m.
Work Step by Step
Here we have n = 12, df = n-1 = 11, x̅ = 147.3 and s = 28.8
Confidence = 95%
α = 1 - 0.95 = 0.05, α/2 = 0.025, $t_{α/2} = 2.2$
$E = 2.2 \times \frac{28.8}{\sqrt 12} = 18.29 $
Lower Bound = x̅ - E = 147.3 - 18.29 = 129.01
Upper Bound = x̅ + E = 147.3 + 18.29 = 165.59
Hence we can say with 95% confidence that the mean diameter of a Douglas fir tree in the western Washington Cascades is between 129.01 and 165.59 m.
