Homework Help is Here – Start Your Trial Now!
Math
Probability
(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] %3D (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.

(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] %3D (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.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
See similar textbooks
icon
Related questions
Question

D and E pl

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 Мean (g) Variance (s) 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 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%).
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 Мean (g) Variance (s) 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 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%).
(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 (s) in this example? Based on this comparison, how effective is the stratification? [use the following formulas: si = E{w;(i - Yst)? and s, = Ew;s ; where w; is the weight for stratum i and ỹst 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] %3D (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.
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 (s) in this example? Based on this comparison, how effective is the stratification? [use the following formulas: si = E{w;(i - Yst)? and s, = Ew;s ; where w; is the weight for stratum i and ỹst 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] %3D (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.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer