7.79 Size of trees in the northern and southern halves. The study of 584 longleaf pine trees in the Wade Tract in Thomas County, Georgia, had several purposes. Are trees in one part of the tract more or less like trees in any other part of the tract or are there differences? In Example 6.1 (page 342), we examined how the trees were distributed in the tract and found that the pattern was not random. In this exercise, we will examine the sizes of the trees. In Exercise 7.33 (page 429), we analyzed the sizes, measured as diameter at breast height (DBH), for a random sample of 40 trees. Here, we divide the tract into northern and southern halves and take random samples of 30 trees from each half. Here are the diameters in centimeters (cm) of the sampled trees:
| 27.8 | 14.5 | 39.1 | 3.2 | 58.8 | 55.5 | 25.0 | 5.4 | 19.0 | 30.6 | |
| North | 15.1 | 3.6 | 28.4 | 15.0 | 2.2 | 14.2 | 44.2 | 25.7 | 11.2 | 46.8 |
| 36.9 | 54.1 | 10.2 | 2.5 | 13.8 | 43.5 | 13.8 | 39.7 | 6.4 | 4.8 | |
| 44.4 | 26.1 | 50.4 | 23.3 | 39.5 | 51.0 | 48.1 | 47.2 | 40.3 | 37.4 | |
| South | 36.8 | 21.7 | 35.7 | 32.0 | 40.4 | 12.8 | 5.6 | 44.3 | 52.9 | 38.0 |
| 2.6 | 44.6 | 45.5 | 29.1 | 18.7 | 7.0 | 43.8 | 28.3 | 36.9 | 51.6 |
(a) Use a back-to-back stemplot and side-by-side boxplots to examine the data graphically. Describe the patterns in the data.
(b) Is it appropriate to use the methods of this section to compare the mean DBH of the trees in the north half of the tract with the mean DBH of the trees in the south half? Give reasons for your answer.
(c) What are appropriate null and alternative hypotheses for comparing the two samples of tree DBHs? Give reasons for your choices.
(d) Perform the significance test. Report the test statistic, the degrees of freedom, and the P-value. Summarize your conclusion.
(e) Find a 95% confidence interval for the difference in mean DBHs. Explain how this interval provides additional information about this problem.