Populations, Samples, and Sampling Methods
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Questions and Answers

What is a population?

  • A subset of a larger group.
  • A group where members have something in common. (correct)
  • A randomly selected group.
  • A small group of individuals.

What is a sample?

  • The entire population
  • A parameter
  • A smaller group of the population (correct)
  • A statistic

What does a parameter describe?

  • The size of the sample.
  • The method of sampling.
  • An entire population. (correct)
  • Only the sample.

What does a statistic describe?

<p>Only the sample. (C)</p> Signup and view all the answers

What is simple random sampling?

<p>Each member of population has an equal chance of being chosen as the sample. (A)</p> Signup and view all the answers

What is involved in stratified random sampling?

<p>Dividing the population into subgroups and sampling from each. (A)</p> Signup and view all the answers

What are the separate groups called in cluster sampling?

<p>Clusters (C)</p> Signup and view all the answers

What is the first step in systematic random sampling?

<p>Random selection of one of the first elements. (A)</p> Signup and view all the answers

What is multistage sampling?

<p>Combining two or more sampling techniques. (D)</p> Signup and view all the answers

In the battery example, what is the statistic?

<p>The average life of 1100 hours of the 100 batteries sampled (B)</p> Signup and view all the answers

In the battery example, what is the parameter?

<p>The average life of the battery they manufacture (A)</p> Signup and view all the answers

What sampling method is used when every 15th student on an alphabetized list is surveyed?

<p>1-in- Systematic random sampling (D)</p> Signup and view all the answers

In a survey, Ms. Cruz wants to know the average weekly allowance of the grade 10 students and only asks 50 students. What is this an example of?

<p>The average weekly allowance of the 50 students. (A)</p> Signup and view all the answers

What type of random sampling is used when 10 students are randomly selected from each grade level?

<p>Stratified Random Sampling (B)</p> Signup and view all the answers

What does the term 'stratum' refer to in stratified sampling?

<p>A subpopulation (B)</p> Signup and view all the answers

What kind of studies can population data best assist in?

<p>Comprehensive demographic studies (D)</p> Signup and view all the answers

Which element is essential for a sample to accurately represent a population?

<p>Random selection (D)</p> Signup and view all the answers

When would cluster sampling instead of sample statistic calculations be most effective?

<p>Assessing easily divided communities (B)</p> Signup and view all the answers

How does parameter estimation aid in larger studies?

<p>Offers population-wide insights (D)</p> Signup and view all the answers

In systematic sampling, if the population is 500 and the desired sample size is 25, what is the sampling interval?

<p>20 (A)</p> Signup and view all the answers

Which sampling method is most suitable when the population is geographically dispersed and data collection is costly?

<p>Cluster sampling (A)</p> Signup and view all the answers

In multistage sampling, what is the primary advantage of combining different sampling techniques?

<p>Enhanced efficiency and precision (D)</p> Signup and view all the answers

A researcher wants to study the reading habits of students in a university. They randomly select 50 students from each academic department (e.g., English, History, Math). Which sampling method are they using?

<p>Stratified sampling (B)</p> Signup and view all the answers

A researcher wants to estimate the average income of households in a city. They divide the city into blocks and randomly select 10 blocks. Then, they collect data from every household within those 10 blocks. Which sampling method are they using?

<p>Cluster sampling (A)</p> Signup and view all the answers

What must occur for simple random sampling to provide each member of the population has an equal opportunity to be selected?

<p>Each member must be labeled (A)</p> Signup and view all the answers

Flashcards

What is a Population?

A group where members share a common characteristic; the complete collection of observations possible.

What is a Sample?

A smaller group or subset taken from the entire population.

What is a Parameter?

Describes a characteristic of an entire population.

What is a Statistic?

Describes a characteristic of a sample only.

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What is Simple Random Sampling?

Each member of the population has an equal chance of being selected.

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What is Stratified Random Sampling?

Divides the population into subgroups (strata) and samples randomly from each.

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What is Cluster Sampling?

The population is divided into groups (clusters) and then clusters are randomly selected.

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What is 1-in-k Systematic Random Sampling?

Randomly selects one of the first k elements, then selects every kth element thereafter.

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What is Multistage Sampling?

Combines two or more sampling techniques.

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Study Notes

Key Definitions

  • A population consists of a group of members with a common characteristic, representing the total set of possible observations.
  • A sample is a smaller group, or a subset, taken from the population.
  • A parameter describes an entire population.
  • A statistic describes only the sample.

Sampling Methods

  • Simple random sampling is the simplest way to get a random sample; each population member has an equal chance of being chosen.
  • To choose a sample, arrange the population elements in order. Use a computer or scientific calculator to generate the required number of random number, the sample comprises elements corresponding to the random numbers.
  • Stratified random sampling involves taking a simple random sample from each subpopulation, known as a stratum.
  • Cluster sampling first divides the population into separate groups called clusters. Then, a simple random sample of clusters is selected from available ones.
  • 1-in-k systematic random sampling involves randomly selecting one of the initial elements in an ordered population. Elements are then selected systematically selecting every kth element thereafter. The value of k is derived by dividing the population size by the desired sample size.
  • Multistage sampling combines two or more probability techniques.

Example 1

  • A quality manager wants to determine the average life of manufactured batteries. Employees tested 100 randomly sampled batteries and found an average life of 1100 hours.
  • 1100 hours represents the statistic because it describes the sample of 100 batteries.
  • The parameter refers to the average lifespan of all batteries produced.

Example 2

  • A university marketing department conducts a satisfaction survey by alphabetizing student names and selecting a random start point, after which every 15th student receives a survey.
  • Selecting every "kth" element defines 1-in-k systematic random sampling, hence this method is employed.

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Description

Understand populations versus samples and parameters versus statistics. Learn about simple random, stratified random, and cluster sampling. Explore 1-in-k systematic random sampling techniques.

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