Answered: Laboratory: Use data of Farms in the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Laboratory: Use data of Farms in the valley of the Jolly Green Giant created in
the laboratory session. This data consisted of 36 farms, each farm having
measurements on the farm acreage and fuel consumption.
a. Select a simple random sample of size 6 (use seed=2010). Using this
sample data:
i. Estimate the mean farm size and mean fuel consumption in Jolly
Green Giant.
ii. Construct 95% confidence intervals for the average farm size and
average fuel consumption for the Jolly Green Giant.
iii. Estimate the total farm size and total fuel consumption in Jolly
Green Giant. Estimate the respective bounds on the error of
estimation.
b. Select a stratified random samples of sizes 2 (for the small farms) and 4
(for the large farms) using seeds provided in the laboratory example.
Using this sample data:
iv. Estimate the mean farm size and mean fuel consumption in Jolly
Green Giant.
v. Construct 95% confidence intervals for the average farm size and
average fuel consumption for the Jolly Green Giant.
vi. Estimate the total farm size and total fuel consumption in Jolly
Green Giant. Estimate the respective bounds on the error of
estimation.
c. How do your estimates in (a) and (b) compare? Explain.

Data from all the Farms in the Valley of the Jolly Green Giant
Obs farm_no acreage fuel consump
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
1
2 100
5
3
4 200
6
800
7 550
8
10
700
9 750
11
12
13
50
17
150
18
700
20
21
22
14 300
23
400
15 200
16
600
650
250
200
19 450
400
450
100
400
350
150
129
200
800
1000
1350
8000
9000
5300
6400
6500
2500
6700
7200
3000
2000
1800
1500
2200
2850
900
1250
3000
900
1300

Obs farm_no acreage fuel consump
24
25
26
27
28
29
30
31
32
33
34
35
36
24
25
26
27
28
29
30
31
32
33
34
35
36
550
100
150
500
450
400
50
100
1200
600
550
800
200
5000
650
2000
4200
5100
6700
600
850
12800
10400
7500
7300
3200

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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