Question 1

The primary advantage of cluster sampling is sampling convenience (and possibly less cost).The downside,however,is that the inferences drawn from a cluster sample can be less accurate,for a given sample size,than for other sampling plans.

Accepted Answer

Cluster sampling is convenient and cost-effective because it involves selecting groups or clusters instead of individual elements, leading to potential savings in time and resources. However, this method can result in less accurate inferences compared to other sampling techniques like stratified or simple random sampling, especially if the clusters are not homogeneous, because it increases the sampling error for a given sample size.

Question 2

In stratified sampling with proportional sample sizes,the proportion of each stratum selected differs from stratum to stratum.

Accepted Answer

In stratified sampling with proportional sample sizes, the proportion of each stratum selected is the same across all strata, reflecting the proportion of each stratum in the total population.

Question 3

Cluster sampling is often less convenient and more costly than other random sampling methods.

Accepted Answer

Cluster sampling can be more convenient and less costly than other random sampling methods, especially when the population is spread out geographically, as it allows for the grouping of participants into clusters.

Question 4

When we sample less than 5% of the population,the finite population correction factor; fpc =  ,is used to modify the formula for the standard error of the sample mean.

Accepted Answer

The answer of When we sample less than 5% of...

Question 5

Systematic sampling is generally similar to simple random sampling in its statistical properties.

Accepted Answer

Systematic sampling, where elements are selected at regular intervals from a sorted list, often yields results similar to simple random sampling in terms of unbiasedness and variance, assuming the list is not ordered in a way that introduces a bias related to the sampling interval.

Question 6

A probability sample is a sample in which the sampling units are chosen from the population by means of a random mechanism such as a random number table.

Accepted Answer

A probability sample is indeed a type of sample where each unit in the population has a known, non-zero chance of being selected, often through random mechanisms like random number tables, ensuring that the sample is representative of the population.

Question 7

The difference between the point estimate and the true value of the population parameter being estimated is called the estimation error.

Accepted Answer

The estimation error is indeed the difference between the point estimate (the single value estimate from a sample) and the true value of the population parameter being estimated. This error reflects how close the estimate is to the actual value.

Question 8

The finite population correction factor is a correction for the standard error when the sample size is fairly large relative to the population size.

Accepted Answer

The finite population correction factor is used to adjust the standard error when the sample size is a significant fraction (usually over 5%) of the total population, reducing the standard error to account for the decreased variability when sampling from a finite population.

Question 9

Simple random sampling can result in under-representation or over-representation of certain segments of the population.This is one of several reasons that simple random samples are almost never used in real applications.

Accepted Answer

Simple random sampling, while theoretically unbiased, can lead to under-representation or over-representation of certain segments due to random chance, especially in smaller sample sizes, making it less practical for ensuring representative data in real-world applications.

Question 10

The standard error of sample mean  is large when the observations in the population are spread out (large  ),but that the standard error can be reduced by taking a smaller sample.

Accepted Answer

The answer of The standard error of sample mean ...

Question 11

In stratified sampling,the population is divided into relatively homogeneous subsets called strata,and then random samples are taken from each stratum.

Accepted Answer

In stratified sampling, the population is indeed divided into subgroups (strata) that are internally homogeneous but heterogeneous between each other, and then random samples are drawn from each of these strata to ensure representation of the entire population.

Question 12

One obvious advantage of stratified sampling is that we obtain separate estimates within each stratum - which we would not obtain if we took a simple random sample from the entire population.A more important advantage is that we can increase the accuracy of the resulting population estimates by using appropriately defined strata.

Accepted Answer

Stratified sampling allows for more accurate population estimates because it ensures that each subgroup (stratum) of the population is adequately represented in the sample, reducing sampling error compared to simple random sampling.

Question 13

Stratified samples are typically not used in real applications because they provide less accurate estimates of population parameters for a given sampling cost.

Accepted Answer

Stratified sampling is often used in real applications because it can provide more accurate estimates of population parameters than simple random sampling, especially when the population is heterogeneous. By dividing the population into homogeneous subgroups and sampling from each subgroup, it ensures that important subgroups are represented in the sample.

Question 14

In cluster sampling,the population is divided into subsets called clusters (such as cities or city blocks),and then a random sample of the clusters is selected.Once the clusters are selected,we typically acquire information from all of the members in each selected cluster.

Accepted Answer

In cluster sampling, the entire population is divided into clusters, and then a random sample of these clusters is selected. After selecting the clusters, data is collected from all members within each of the chosen clusters, making the explanation accurate.

Question 15

We can measure the accuracy of judgmental samples by applying some simple rules of probability.This way,judgmental samples are not likely to contain our built-in biases.

Accepted Answer

Judgmental sampling, by definition, relies on the judgment of the person conducting the sampling, which inherently includes their biases, making it difficult to measure accuracy through simple rules of probability.

Question 16

Simple random samples are samples in which every possible sample of size n from the population has the same probability of being chosen.

Accepted Answer

Simple random samples are indeed defined by the characteristic that every possible sample of the specified size (n) from the population has an equal chance of being selected. This ensures that the sample is representative of the population, minimizing selection bias.

Question 17

A point estimate is a single numeric value,a "best guess" of a population parameter,calculated from the sample data.

Accepted Answer

A point estimate indeed refers to a single numeric value derived from sample data, which serves as the best guess or estimate of a population parameter.

Question 18

A list of all members of the population from which we can choose a sample is called a frame,and the potential sample members are called sampling units.

Accepted Answer

A frame is indeed a list of all members of the population from which a sample can be chosen, and the individual members of this population that can be selected for the sample are referred to as sampling units.

Question 19

In systematic sampling,one of the first k members is selected randomly,and then every k^th member after this one is selected.The value k is called the sampling interval and equals the ratio N / n,where N is the population size and n is the desired sample size.

Accepted Answer

In systematic sampling, the sampling interval (k) is indeed calculated as the ratio of the population size (N) to the desired sample size (n), ensuring a spread of the sample across the entire population.

Question 20

A simple random sample is one where each member of the population has a known chance (this may differ from one member to another)or probability of being chosen.

Accepted Answer

In a simple random sample, each member of the population has an equal chance of being chosen, not differing probabilities.

Quiz 7: Sampling and Sampling Distributions