/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 41 Sampling A mazon For ests. Strat... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Sampling A mazon For ests. Stratified samples are widely used to study large areas of forest. Based on satellite images, a forest area in the Amazon basin is divided into 14 types. Foresters studied the four most commercially valuable types: alluvial climax forests of quality levels 1, 2, and 3 , and mature secondary forest. They divided the area of each type into large parcels, chose parcels of each type at random, and counted tree species in a 20 - by 25 -meter rectangle randomly placed within each parcel selected. Here is some detail: Choose the stratified sample of 18 parcels. Be sure to explain how you assigned labels to parcels. If you use Table B, start at line \(112 .\)

Short Answer

Expert verified
Select 18 parcels using stratified sampling, dividing selections between the four forest types based on proportional representation.

Step by step solution

01

Understand Stratified Sampling

Stratified sampling involves dividing the population into distinct subgroups, or strata, that share a common characteristic, and then randomly sampling from each stratum. In this exercise, the forest is divided into four types, each representing a different stratum.
02

Determine the Number of Parcels in Each Stratum

The problem states that we're focusing on four forest types: alluvial climax forests of quality levels 1, 2, and 3, and mature secondary forests. For a balanced stratified sample, decide how many parcels to choose from each stratum. For example, if there are 14 parcels of each type, select an equal number of parcels from each type to maintain proportionality.
03

Label the Parcels

Assign a unique label to each parcel within a stratum to identify them. For example, if each type has 14 parcels, you can label parcels for quality level 1 as 1 to 14, quality level 2 as 15 to 28, and so on.
04

Random Selection from Each Stratum

Use a random method, such as a random number table (like Table B) or computational tool, to select parcels. Starting at line 112 of the table, find random numbers that match your labeled parcels. Ignore any numbers that fall outside the labeled range or are repeated.
05

Select Parcels from Table B

Using Table B from line 112, select unique numbers corresponding to each stratum until you've chosen 18 parcels in total (e.g., 4 from each quality level and 6 from mature secondary forests if stratified proportionally). Keep track of selected numbers ensuring no repetition.
06

Document Selected Parcels

Record the chosen parcels clearly, indicating the number of parcels selected from each forest type and ensuring that the sum equals 18.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Forest Sampling
When researchers study vast areas like forests, it’s essential to use effective sampling methods to gain accurate insights. Forest sampling, a practical approach often applied in ecological studies, involves collecting data from a portion of the entire forest to make conclusions about the whole. This method helps ecologists and foresters understand the biodiversity, tree species density, and ecological changes without examining every acre. In our exercise, researchers used **stratified sampling**. They divided the Amazon forest into four significant and valuable types of forest.

By focusing on these types, researchers can target areas most likely to yield critical information on species distribution and forest health. This approach makes studies more feasible and cost-effective.
Random Selection Process
The essence of a random selection process lies in its ability to remove bias and provide each element in the population with an equal chance of selection. This process is crucial in sampling because it assures that the sample accurately represents the entire population, or in our case, the whole forest region. For stratified sampling, once the forest is divided into strata, parcels from each stratum are selected randomly.

Randomly selecting parcels ensures that the study's results are not skewed by predetermined or accidental biases. In this exercise, using techniques like a random number table ensures parcels are chosen fairly. This method involves starting at a specific point in the table and choosing numbers that correlate with the numerical labels given to each parcel. Remember, if a number doesn’t correspond with any parcel or repeats, it’s ignored to maintain randomness.

This step-by-step precision in selection enhances the validity and reliability of the results.
Statistical Sampling Methods
Statistical sampling methods, such as stratified sampling used here, are essential tools in research studies. Each type of sampling serves different needs depending on the research objective, the population size, and its diversity. Stratified sampling, in particular, ensures diverse representation by dividing the population into distinct subgroups. This process allows researchers to gather insights accurately reflecting each subgroup within the broader population.

In the context of forest sampling, this method is particularly beneficial for capturing variations across different forest types. It ensures that each area type within the forest is proportionately represented, allowing for more nuanced findings. Other types of statistical sampling methods might include simple random sampling, where each member of a population has an equal chance of selection, or systematic sampling, which could select every 10th parcel in a list.

By choosing the appropriate sampling method, researchers can enhance their ability to make valid inferences about the entire population from their sample data.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

An opinion poll calls 2000 randomly chosen residential telephone numbers in Portland and asks to speak with an adult member of the household. The interviewer asks, "How many movies have you watched in a movie theater in the past 12 months?" In all, 831 people respond. The sample in this study is a. all adults living in Portland. b. the 2000 residential phone numbers called. c. the 831 people who responded.

Nonresponse. Exercise \(8.10\) discusses the Pew Research Center survey Teens, Social Media \(\&\) Technology conducted in the spring of 2018 . The report mentions that 743 teens completed the survey and that the response rate for teens was \(18 \% .27\) Approximately how many teens must have been recruited for the survey for a response rate of \(18 \% ?\)

Sampling on Campus. You would like to start a club for psychology majors on campus, and you are interested in finding out what proportion of psychology majors would join. The dues would be \(\$ 35\) and used to pay for speakers to come to campus. You ask five psychology majors from your senior psychology honors seminar whether they would be interested in joining this club and find that four of the five students questioned are interested. Is this sampling method biased, and if so, what is the likely direction of bias?

Student Opinions. A university has 30,000 undergraduate and 10,000 graduate students. A survey of student opinion concerning health care benefits for domestic partners of students selects 300 of the 30,000 undergraduate students at random and then separately selects 100 of the 10,000 graduate students at random. The 400 students chosen make up the sample. a. What is the probability that any of the 30,000 undergraduates is in your random sample of 300 undergraduates selected? What is the probability that any of the 10,000 graduate students is in your random sample of 100 graduate students selected? b. If you have done the calculations correctly in part (a), the probability of any student at the university being selected is the same. Why is your sample of 400 students from the university not an SRS of students? Explain.

You must choose an SRS of 10 of the 440 retail outlets in New York that sell your company's products. How would you label this population to select a simple random sample? a. \(001,002,003, \ldots, 439,440\) b. \(000,001,002, \ldots, 439,440\) c. \(1,2, \ldots, 439,440\)

See all solutions

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.