7.33 Tree diameter confidence interval. A study of 584 longleaf pine trees in the Wade Tract in Thomas County, Georgia, is described in Example 6.1 (page 342). For each tree in the tract, the researchers measured the diameter at breast height (DBH). This is the diameter of the tree at a height of 4.5 feet, and the units are centimeters (cm). Only trees with DBH greater than 1.5 cm were sampled. Here are the diameters of a random sample of 40 of these trees:
| 10.5 | 13.3 | 26.0 | 18.3 | 52.2 | 9.2 | 26.1 | 17.6 | 40.5 | 31.8 |
| 47.2 | 11.4 | 2.7 | 69.3 | 44.4 | 16.9 | 35.7 | 5.4 | 44.2 | 2.2 |
| 4.3 | 7.8 | 38.1 | 2.2 | 11.4 | 51.5 | 4.9 | 39.7 | 32.6 | 51.8 |
| 43.6 | 2.3 | 44.6 | 31.5 | 40.3 | 22.3 | 43.3 | 37.5 | 29.1 | 27.9 |
(a) Use a histogram or stemplot and a boxplot to examine the distribution of DBHs. Include a Normal quantile plot if you have the necessary software. Write a careful description of the distribution.
(b) Is it appropriate to use the methods of this section to find a 95% confidence interval for the mean DBH of all trees in the Wade Tract? Explain why or why not.
(c) Report the mean with the margin of error and the confidence interval. Write a short summary describing the meaning of the confidence interval.
(d) Do you think these results would apply to other similar trees in the same area? Give reasons for your answer.