A forestry company experiments with the rate of growth of different types of tre
ID: 3204899 • Letter: A
Question
A forestry company experiments with the rate of growth of different types of trees. It has planted 48treesin one longline alongside a road. The trees are alternately of types A and B. After 2 years, the company wants to know the average height of all trees.
The length of all 48 trees can be found in the table below:
629 353 664 351 633 314 660 381 640 366 696 348 681 307 633 337 663 331 609 338 675 361 696 304 647 366 669 384 669 389 693 324 698 309 602 341 671 352 663 344 671 342 627 323 612 376 629 363
a. Compute the mean length and the standard deviation of all 48 trees.
b. Draw a simple random sample without replacement of size n = 8. Use the table with random numbers below. Work row-wise and use only the first two digits of each group of five digits. Compute the sample mean and the sample standard deviation 94830 56343 45319 85736 71418 47124 11027 15995 68274 45056 17838 77075 43361 69690 40430 74734 66769 26999 58469 75469 82789 17393 52499 87798 09954 02758 41015 87161 52600 94263 64429 42371 14248 93327 86923 12453 46224 85187 66357 14125 76370 72909 63535 42073 26337 96565 38496 28701 52074 21346
c. Draw a systematic sample of size 8. Use the value b = 3 as starting point. Compute the sample mean and the sample standard deviation.
d. Compare the results of exercises (b) and (c) with those of exercise. Explain observed differences and/or similarities.
Explanation / Answer
a)
x
xi-x
xi-x^2
629
128.29
16458.32
353
-147.71
21818.24
664
163.29
26663.62
351
-149.71
22413.08
633
132.29
17500.64
314
-186.71
34860.62
660
159.29
25373.3
381
-119.71
14330.48
640
139.29
19401.7
366
-134.71
18146.78
696
195.29
38138.18
348
-152.71
23320.34
681
180.29
32504.48
307
-193.71
37523.56
633
132.29
17500.64
337
-163.71
26800.96
663
162.29
26338.04
331
-169.71
28801.48
609
108.29
11726.72
338
-162.71
26474.54
675
174.29
30377
361
-139.71
19518.88
696
195.29
38138.18
304
-196.71
38694.82
647
146.29
21400.76
366
-134.71
18146.78
669
168.29
28321.52
384
-116.71
13621.22
669
168.29
28321.52
389
-111.71
12479.12
693
192.29
36975.44
324
-176.71
31226.42
698
197.29
38923.34
309
-191.71
36752.72
602
101.29
10259.66
341
-159.71
25507.28
671
170.29
28998.68
352
-148.71
22114.66
663
162.29
26338.04
344
-156.71
24558.02
671
170.29
28998.68
342
-158.71
25188.86
627
126.29
15949.16
323
-177.71
31580.84
612
111.29
12385.46
376
-124.71
15552.58
629
128.29
16458.32
363
-137.71
18964.04
24034
1181848
500.7083
Mean
24621.83
156.9135
S.D
b)
x
xi-x
xi-x^2
94
41.375
1711.891
85
32.375
1048.141
15
-37.625
1415.641
40
-12.625
159.3906
87
34.375
1181.641
2
-50.625
2562.891
72
19.375
375.3906
26
-26.625
708.8906
421
9163.875
52.625
Mean
1309.125
36.18183
S.D
c)
x
xi-x
xi-x^2
3
-17
289
5
-15
225
9
-11
121
12
-8
64
20
0
0
31
11
121
37
17
289
43
23
529
160
1638
20
Mean
234
15.29706
S.D
d)
Mean=Ex/n
S.D(population)=sqrt(E(xi-x)^2/n)
S.D(sample)=sqrt(E(xi-x)^2/n-1)
As we can see that higher the n, the difference between mean and standard deviation is more as compared to n being small as we can see in b and c. Also, in case of standard deviation, n-1 would be taken for sample S.D whereas in population it would be divided by n.
x
xi-x
xi-x^2
629
128.29
16458.32
353
-147.71
21818.24
664
163.29
26663.62
351
-149.71
22413.08
633
132.29
17500.64
314
-186.71
34860.62
660
159.29
25373.3
381
-119.71
14330.48
640
139.29
19401.7
366
-134.71
18146.78
696
195.29
38138.18
348
-152.71
23320.34
681
180.29
32504.48
307
-193.71
37523.56
633
132.29
17500.64
337
-163.71
26800.96
663
162.29
26338.04
331
-169.71
28801.48
609
108.29
11726.72
338
-162.71
26474.54
675
174.29
30377
361
-139.71
19518.88
696
195.29
38138.18
304
-196.71
38694.82
647
146.29
21400.76
366
-134.71
18146.78
669
168.29
28321.52
384
-116.71
13621.22
669
168.29
28321.52
389
-111.71
12479.12
693
192.29
36975.44
324
-176.71
31226.42
698
197.29
38923.34
309
-191.71
36752.72
602
101.29
10259.66
341
-159.71
25507.28
671
170.29
28998.68
352
-148.71
22114.66
663
162.29
26338.04
344
-156.71
24558.02
671
170.29
28998.68
342
-158.71
25188.86
627
126.29
15949.16
323
-177.71
31580.84
612
111.29
12385.46
376
-124.71
15552.58
629
128.29
16458.32
363
-137.71
18964.04
24034
1181848
500.7083
Mean
24621.83
156.9135
S.D
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