18 Questions
What is the purpose of selecting a sample?
To collect data to answer a research question about a population
What is a frame in the context of sampling?
A list of the elements that the sample will be selected from
What is the primary reason for using sampling distributions?
To provide good estimates of population characteristics
What is stratified random sampling?
A method of sampling where the population is divided into smaller groups called strata
What is cluster sampling?
A method of sampling where the population is divided into clusters based on similarity
What is systematic sampling?
A method of sampling where elements are selected systematically
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
In the context of sampling distributions, what does E(p) = p represent?
The expected value of the population proportion
What is used to make inferences about the value of p in sampling distributions?
The sample data
When can the sampling distribution of p be approximated by a normal distribution?
When the sample size is large
Which sampling method involves dividing the population into subgroups and then taking random samples from each subgroup?
Stratified Random Sampling
In cluster sampling, how are clusters selected from the population?
By dividing the population into groups and then randomly selecting whole groups
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
What does the sampling distribution of x represent?
The distribution of the sample mean x across all possible samples
In point estimation, what does E( x ) = μ signify?
The value used to estimate properties of the population mean
What does σx represent in the context of sampling distributions?
The standard error of the mean
When is a finite population treated as infinite in calculating σx?
When n/N < 0.05
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
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.
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.
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