Chapter 8 - QMB2100 Flashcards
What is the primarily goal of sampling?
Producing a sample that is unbiased and hence a good representation of the population.
What are 4 practical reasons to sample from a population?
- To contact the whole population would be time consuming.
- The cost of studying all the items in a population may be prohibitive.
- The physical impossibility of checking all items in the population.
- The destructive nature of some tests.
What is the simple random sampling method?
A method in which a sample is selected so that each item or person in the population has the same probability or chance of being included.
What are some functions used in excel to generate random numbers?
=rand(), =randbetween()
What is systematic random sampling?
A random starting point is selected, and then every kth member of the population is selected.
When is systematic random sampling not useful?
When the physical order of the population is related to the population characteristic; it could create bias.
When is simple random sampling not useful?
When assigning a random number to a population of customers is impossible.
When do we use stratified random sampling?
When a population can be clearly divided into groups based on some characteristic.
Why should stratified random sampling be used?
It guarantees each group is represented in the sample.
How are the groups in stratified random sampling called?
Strata.
What is stratified random sampling?
A population is divided into subgroups, called strata, and a sample is randomly selected from each stratum using simple random sampling.
What is the advantage of stratified random sampling?
More accurately reflecting the characteristics of the population than does simple random sampling or systematic random sampling.
What is cluster sampling?
When a population is divided into clusters using naturally occurring geographic or other boundaries. Then, clusters are randomly selected and a sample is collected by randomly selecting from each cluster.
When is cluster sampling used?
When a population is scattered over a large geographic area.
What is sampling error?
The difference between a sample statistic and its corresponding population parameter; x̄ - μ.
Why the sample mean and standard deviation are random variables?
Because each sample is different, each will have a different mean and standard deviation. Therefore, sample statistics are random variables that can be described with probability distributions.
What is sampling distribution of the sample mean?
A probability of all possible sample means, calculated from all possible random samples of a given sample size.
How do you find the mean of all the samples?
μx̄ = sum of all sample means / total number of samples
Describe 3 important relationships between the population distribution and the sampling distribution of the sample mean.
- The mean of the sample mean is exactly equal to the population mean.
- The dispersion of the sampling distribution of the sample mean is narrower than the population distribution.
- The sampling distribution of the sample mean tends to become bell shaped and to approximate the normal probability distribution.
What is the central limit theorem?
If all samples of a particular size are selected from any population, the sampling distribution of the sample mean is approximately a normal distribution. This approximation improves with larger samples.
What is the standard error of the mean?
The standard deviation of the sample means; σx̄ = σ / √(n) where σx̄ is the standard error, σ is the standard deviation in the population, and n is the total samples.
What are the 2 conditions for the sampling distribution to be normally distributed?
- When samples are taken from a population known to follow a normal distribution; size of the sample is not a factor.
- When the shape of the distribution is not known, sample size is important. The sampling distribution will be normally distributed as the sample size approaches infinity. In fact, a sampling distribution will be close to a normal distribution with samples of at least 30 observations.
How do you find the z-value of x̄ when the population standard deviation is known?
z = (x̄ - μ) / (σ / √(n))
What is the sample proportion?
The fraction, ratio, or percent indicating the part of the sample or the population having a particular trait of interest.
p = x/n; where p is the sample proportion, x is the count or number of successful outcomes, and n is the sample size or total count of outcomes.
Describe 3 characteristics of the sample proportion.
- It estimates the true population π.
- It is a random variable and it is described with a probability distribution.
- If the sample size is large enough, we can apply the central limit theorem.
What are the 2 requirements to determine if the sample size is large enough to apply the central limit theorem for a sample proportion?
- nπ more than or equals to 5
- nπ(1 - π) more than or equals to 5
What is the standard error of the proportion?
σp = sqrt (π(1-π)/n)
How do you find the z-value for a sample proportion?
z = (p - π) / sqrt(π(1-π)/n)
