Question

7.136  Analysis of tree size using the complete data set. The data used in Exercises 7.33 (page 429), 7.79, and 7.80 (page 459) were obtained by taking SRSs from the 584 longleaf pine trees that were measured in the Wade Tract. The entire data set is given in the WADE data set. Find the 95% confidence interval for the mean DBH using the entire data set, and compare this interval with the one that you calculated in Exercise 7.33. Write a report about these data. Include comments on the effect of the sample size on the margin of error, the distribution of the data, the appropriateness of the Normality-based methods for this problem, and the generalizability of the results to other similar stands of longleaf pine or other kinds of trees in this area of the United States and other areas.

Data from exercice 7.33

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

Data from exercie 7.79.

	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

Data from exercice 7.80 .

23.5	43.5	6.6	11.5	17.2	38.7	2.3	31.5	10.5	23.7
East	13.8	5.2	31.5	22.1	6.7	2.6	6.3	51.1	5.4	9.0
	43.0	8.7	22.8	2.9	22.3	43.8	48.1	46.5	39.8	10.9
	17.2	44.6	44.1	35.5	51.0	21.6	44.1	11.2	36.0	42.1
West	3.2	25.5	36.5	39.0	25.9	20.8	3.2	57.7	43.3	58.0
	21.7	35.6	30.9	40.6	30.7	35.6	18.2	2.9	20.4	11.4

Answer 1

Exercise 7.33:

27.29	mean Data
17.71	std. dev.
2.80	std. error
40	n
39	df
21.63	confidence interval 95.% lower
32.95	confidence interval 95.% upper
5.66	margin of error

The 95% confidence interval is between 21.63 and 32.95.

The normal probability plot is:

The data is normally distributed.

The margin of error is 5.66 and the sample size is 40.

Entire data set:

27.49	mean Data
16.72	std. dev.
1.32	std. error
160	n
159	df
24.88	confidence interval 95.% lower
30.10	confidence interval 95.% upper
2.61	margin of error

The 95% confidence interval is between 24.88 and 30.10.

The normal probability plot is:

The data is normally distributed.

The margin of error is 2.61 and the sample size is 160.

It is clear that with the increase in sample size, the margin of error decreases and the width of confidence interval decreases.