Question 1

It is often not feasible to study the entire population because it is impossible to observe all the items in the population.

Accepted Answer

Studying the entire population may not be practical due to factors such as time, cost, and resources. Therefore, researchers typically collect data from a representative sample of the population.

Question 2

The items or individuals of the population are arranged in a file drawer alphabetically by date received.A random starting point is selected and then every k^th member of the population is selected for the sample.This sampling method is called simple random sampling.

Accepted Answer

The sampling method described is systematic sampling, not simple random sampling. In simple random sampling, each member of the population has an equal chance of being selected for the sample.

Question 3

Sampling a population is often necessary because the cost of studying all the items in the population is prohibitive.

Accepted Answer

Sampling allows for a smaller and more manageable portion of the population to be studied, which is often more cost-effective and practical than studying the entire population.

Question 4

If the size of a sample equals the size of the population,we would not expect any error in estimating the population parameter.

Accepted Answer

If the size of a sample equals the size of the population, this is called a census. While a census can provide an accurate estimate of the population parameter, there is still the possibility of error due to sampling variability or errors in data collection. However, the margin of error would be expected to be smaller than if a smaller sample size were used.

Question 5

A simple random sample assumes that each item or person in the population has an equal chance of being included.

Accepted Answer

A simple random sample is designed in such a way that every item or person in the population has an equal chance of being selected. Therefore, statement A is correct.

Question 6

When systematic random sampling is used,the central limit theorem cannot be applied.

Accepted Answer

The central limit theorem can be applied with systematic random sampling as long as the sample is sufficiently large and meets the assumptions of the theorem.

Question 7

The central limit theorem implies that for adequate sample size,the sampling distribution of the sample mean is approximately normal.

Accepted Answer

The central limit theorem states that regardless of the distribution of the population, the sampling distribution of the sample mean tends to be approximately normal for large sample sizes (typically 30 or greater).

Question 8

In stratified random sampling,a population is divided into strata using naturally occurring geographic or other boundaries.Then strata are randomly selected and a random sample is collected from each strata.

Accepted Answer

In stratified random sampling, a population is divided into strata based on specific characteristics or criteria, not necessarily geographic or other natural boundaries. Then, a random sample is collected from each stratum to ensure representation of the entire population.

Question 9

The standard error of the mean is also called sampling error.

Accepted Answer

The answer of The standard error of the mean is...

Question 10

In stratified random sampling,a population is divided into subgroups called strata and a sample is randomly selected from each stratum.

Accepted Answer

In stratified random sampling, the population is indeed divided into subgroups called strata and a sample is selected randomly from each stratum.

Question 11

If a population is not normally distributed,the sampling distribution of the sample means tends to approximate a normal distribution.

Accepted Answer

The Central Limit Theorem states that regardless of the shape of the population distribution, the sampling distribution of the sample means tends to approximate a normal distribution as the sample size increases.

Question 12

A sampling distribution of the means is a probability distribution consisting of a list of all possible sample means of a given sample size selected from a population and the probability of occurrence associated with each sample mean.

Accepted Answer

This statement accurately describes a sampling distribution of the means.

Question 13

The central limit theorem implies that for samples of size one or two,we can infer that the sampling distribution of the sample mean is approximately normal.

Accepted Answer

The central limit theorem applies to samples of size n>30, not for samples of size one or two. For small sample sizes, the distribution of the sample mean may not be normal and may need other methods to estimate the population mean.

Question 14

When using systematic random sampling,the sampling error will be zero.

Accepted Answer

Systematic random sampling can still have sampling errors, particularly if there is a pattern or bias in the selection process. However, it generally has less sampling error than simple random sampling.

Question 15

For a simple random sample,each item in the population has an equal chance of being chosen.

Accepted Answer

In a simple random sample, every individual in the population has an equal probability of being selected, which is the definition of what a simple random sample is. Therefore, the statement is true.

Question 16

We can expect some difference between sample statistics and the corresponding population parameters.This difference is called the sampling error.

Accepted Answer

Sampling error is the difference between a sample statistic and the corresponding population parameter, caused by random variation in the selection of a sample from a population.

Question 17

When cluster sampling is used,the central limit theorem cannot be applied.

Accepted Answer

The central limit theorem can still be applied in cluster sampling, as long as the clusters are randomly selected and the sample size within each cluster is sufficiently large.

Question 18

In cluster sampling,a population is divided into subgroups called clusters and a sample is randomly selected from each cluster.

Accepted Answer

In cluster sampling, the entire population is divided into clusters, but instead of sampling from each cluster, a random selection of clusters is chosen, and all individuals within these selected clusters are surveyed or studied.

Question 19

When using stratified random sampling,the sampling error will be zero.

Accepted Answer

While stratified random sampling can reduce the sampling error compared to simple random sampling, it is unlikely to completely eliminate it. There is always some level of error present in any sampling method.

Question 20

In cluster sampling,a population is divided into clusters using naturally occurring geographic or other boundaries.Then clusters are randomly selected and a random sample is collected from each cluster.

Accepted Answer

This is a correct description of cluster sampling.

Quiz 8: Sampling Methods and the Central Limit Theorem