Sampling and Sampling Distributions (Chapter 7)

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Questions and Answers

What is the purpose of selecting a sample?

To collect data about the entire population

To collect data to answer a research question about a population (correct)

To estimate population characteristics without any errors

To select elements from a process

What is a frame in the context of sampling?

A subset of the population

A set of all the elements of interest

A list of all elements in a population

A list of the elements that the sample will be selected from (correct)

What is the primary reason for using sampling distributions?

To eliminate the need for sampling

To provide good estimates of population characteristics (correct)

To estimate population characteristics with no error

To provide exact values of population characteristics

What is stratified random sampling?

A method of sampling where the population is divided into smaller groups called strata Signup and view all the answers

What is cluster sampling?

A method of sampling where the population is divided into clusters based on similarity Signup and view all the answers

What is systematic sampling?

A method of sampling where elements are selected systematically Signup and view all the answers

What does the sampling distribution of x represent?

The values of x that have less variability and tend to be closer to the population mean Signup and view all the answers

In the context of sampling distributions, what does E(p) = p represent?

The expected value of the population proportion Signup and view all the answers

What is used to make inferences about the value of p in sampling distributions?

The sample data Signup and view all the answers

When can the sampling distribution of p be approximated by a normal distribution?

When the sample size is large Signup and view all the answers

Which sampling method involves dividing the population into subgroups and then taking random samples from each subgroup?

Stratified Random Sampling Signup and view all the answers

In cluster sampling, how are clusters selected from the population?

By dividing the population into groups and then randomly selecting whole groups Signup and view all the answers

What is the purpose of ensuring that the targeted population and the sampled population are in close agreement in sampling?

To make accurate inferences about the population from the sample Signup and view all the answers

What does the sampling distribution of x represent?

The distribution of the sample mean x across all possible samples Signup and view all the answers

In point estimation, what does E( x ) = μ signify?

The value used to estimate properties of the population mean Signup and view all the answers

What does σx represent in the context of sampling distributions?

The standard error of the mean Signup and view all the answers

When is a finite population treated as infinite in calculating σx?

When n/N < 0.05 Signup and view all the answers

What is the purpose of the finite population correction factor (N - n)/(N - 1) in calculating σx?

To adjust for treating a finite population as infinite Signup and view all the answers

Study Notes

Introduction to Sampling

A population is the set of all elements of interest.
A sample is a subset of the population.
An element is the entity on which data are collected.
A frame is a list of the elements that the sample will be selected from.
The reason we select a sample is to collect data to answer a research question about a population.

Sampling Distribution of x

The sampling distribution of x is the probability distribution of all possible values of the sample mean x.
Expected Value of x: E(x) = μ
The value of x is used to make inferences about the value of μ.
Standard Deviation of x: σx = σ / √n (for infinite population)
σx = (σ √(N - n)) / (n √(N - 1)) (for finite population)
The finite population correction factor is (N - n) / (N - 1).
A finite population is treated as being infinite if n/N < 0.05.

Example of Sampling Distribution of x

For a sample size of 100, the standard error of the mean is smaller, and the values of x have less variability and tend to be closer to the population mean than the values of x with a sample size of 30.

Sampling Distribution of p

The sampling distribution of p is the probability distribution of all possible values of the sample proportion p.
Expected Value of p: E(p) = p
The value of p is used to make inferences about the value of p.
Standard Deviation of p: σp = √(p(1 - p)) / √n (for infinite population)
σp = √(p(1 - p) * (N - n)) / (n √(N - 1)) (for finite population)
The sampling distribution of p can be approximated by a normal distribution whenever the sample size is large.

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Description

Test your knowledge on sampling methods, point estimation, and sampling distributions as covered in Chapter 7 of the book 'Contemporary Business Statistics, 3e'. This quiz includes questions on selecting samples, introduction to sampling distributions, and more.