4. Use the data provided in Table 1 to answer questions 4(a)-4(e): Table 1. Seaweed (Ulva) biomass for a reef flat in the Philippines [quadrat size 0.25 m2; Hoisaeter and Matthiesen (1979)]. Stratum Biomass (g) Stratum Area (m²) Sample Size Mean (g) Variance (s³) I 2175 9. 0.5889 0.1661 II 3996 14 19.3857 179.1121 III 1590 7 2.1429 3.7962 IV 1039 6. 0.2000 0.1120 (a) First, calculate strata weights based on the size (area) of each stratum (b) Calculate the stratified mean for Ulva biomass per quadrat. How does this compare to the mean if the authors had used a simple random sampling (SRS) design? [hint: ỹSRS where n¡ and ỹ; are the sample size and stratum mean, respectively, for the ith stratum] (c) Now calculate the standard error for the stratified mean (note: you can ignore the finite population correction factor since the area sampled is less than 5%: area sampled = 100*35*0.25 m²/8800 m² = 0.1%).
4. Use the data provided in Table 1 to answer questions 4(a)-4(e): Table 1. Seaweed (Ulva) biomass for a reef flat in the Philippines [quadrat size 0.25 m2; Hoisaeter and Matthiesen (1979)]. Stratum Biomass (g) Stratum Area (m²) Sample Size Mean (g) Variance (s³) I 2175 9. 0.5889 0.1661 II 3996 14 19.3857 179.1121 III 1590 7 2.1429 3.7962 IV 1039 6. 0.2000 0.1120 (a) First, calculate strata weights based on the size (area) of each stratum (b) Calculate the stratified mean for Ulva biomass per quadrat. How does this compare to the mean if the authors had used a simple random sampling (SRS) design? [hint: ỹSRS where n¡ and ỹ; are the sample size and stratum mean, respectively, for the ith stratum] (c) Now calculate the standard error for the stratified mean (note: you can ignore the finite population correction factor since the area sampled is less than 5%: area sampled = 100*35*0.25 m²/8800 m² = 0.1%).
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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![(c) Now calculate the standard error for the stratified mean (note: you can ignore the finite
population correction factor since the area sampled is less than 5%: area sampled =
100*35*0.25 m²/8800 m² = 0.1%).
%3D
Stratified sampling provides gains in precision when strata are relatively homogeneous; i.e.
the majority of the population variance is partitioned into the between-strata variance. How
does the between-strata variance (s) compare to the within-strata variance (sw) in this
example? Based on this comparison, how effective is the stratification? [use the following
formulas: s = Ew;(yi - Yst)? and s, = Efw;si ; where w; is the weight for stratum i
and yst is the stratified mean]
(d) The mean biomass per quadrat is not a very meaningful number. Estimate the total biomass
(g) of Ulva for the entire reef flat and the standard error for the total biomass. [hint: total
number of possible quadrats
total area / quadrat size]
(e) Another more meaningful number would be the mean density of Ulva: estimate the mean
density (g m2) of Ulva and the standard error for the estimated density.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcd617b0d-2424-4a34-8571-67fe540a0678%2F8ea23a33-f80f-4bd9-8ae2-427364d89dec%2Frha14ms_processed.png&w=3840&q=75)
Transcribed Image Text:(c) Now calculate the standard error for the stratified mean (note: you can ignore the finite
population correction factor since the area sampled is less than 5%: area sampled =
100*35*0.25 m²/8800 m² = 0.1%).
%3D
Stratified sampling provides gains in precision when strata are relatively homogeneous; i.e.
the majority of the population variance is partitioned into the between-strata variance. How
does the between-strata variance (s) compare to the within-strata variance (sw) in this
example? Based on this comparison, how effective is the stratification? [use the following
formulas: s = Ew;(yi - Yst)? and s, = Efw;si ; where w; is the weight for stratum i
and yst is the stratified mean]
(d) The mean biomass per quadrat is not a very meaningful number. Estimate the total biomass
(g) of Ulva for the entire reef flat and the standard error for the total biomass. [hint: total
number of possible quadrats
total area / quadrat size]
(e) Another more meaningful number would be the mean density of Ulva: estimate the mean
density (g m2) of Ulva and the standard error for the estimated density.
![4. Use the data provided in Table 1 to answer questions 4(a)-4(e):
Table 1. Seaweed (Ulva) biomass for a reef flat in the Philippines
[quadrat size 0.25 m?; Hoisaeter and Matthiesen (1979)].
Stratum Biomass (g)
Stratum
Area (m?) Sample Size
Mean (g)
Variance (s?)
I
2175
0.5889
0.1661
II
3996
14
19.3857
179.1121
III
1590
7
2.1429
3.7962
IV
1039
0.2000
0.1120
(a) First, calculate strata weights based on the size (area) of each stratum
(b) Calculate the stratified mean for Ulva biomass per quadrat. How does this compare to the
mean if the authors had used a simple random sampling (SRS) design? [hint: ỹSRS
where n; and ỹ¡ are the sample size and stratum mean, respectively, for the ith stratum]
(c) Now calculate the standard error for the stratified mean (note: you can ignore the finite
population correction factor since the area sampled is less than 5%: area sampled =
100*35*0.25 m²/8800 m? = 0.1%).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcd617b0d-2424-4a34-8571-67fe540a0678%2F8ea23a33-f80f-4bd9-8ae2-427364d89dec%2Ffmv7ef_processed.png&w=3840&q=75)
Transcribed Image Text:4. Use the data provided in Table 1 to answer questions 4(a)-4(e):
Table 1. Seaweed (Ulva) biomass for a reef flat in the Philippines
[quadrat size 0.25 m?; Hoisaeter and Matthiesen (1979)].
Stratum Biomass (g)
Stratum
Area (m?) Sample Size
Mean (g)
Variance (s?)
I
2175
0.5889
0.1661
II
3996
14
19.3857
179.1121
III
1590
7
2.1429
3.7962
IV
1039
0.2000
0.1120
(a) First, calculate strata weights based on the size (area) of each stratum
(b) Calculate the stratified mean for Ulva biomass per quadrat. How does this compare to the
mean if the authors had used a simple random sampling (SRS) design? [hint: ỹSRS
where n; and ỹ¡ are the sample size and stratum mean, respectively, for the ith stratum]
(c) Now calculate the standard error for the stratified mean (note: you can ignore the finite
population correction factor since the area sampled is less than 5%: area sampled =
100*35*0.25 m²/8800 m? = 0.1%).
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