Question 1

In the sampling distribution of the sample means, the standard error of the mean will vary according to the size of the sample. As the sample size, n, gets larger, the variability of the sampling distribution of the means gets larger.

Accepted Answer

As the sample size, n, gets larger, the variability of the sampling distribution of the means decreases and the standard error of the mean decreases.

Question 2

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 the sample statistics and the corresponding population parameters. It is a natural and expected occurrence when taking a sample from a larger population. Therefore, the statement is true.

Question 3

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

Accepted Answer

The standard error of the mean measures the dispersion of sample means around the population mean, while the term "sampling error" refers to the discrepancy between a sample statistic and its corresponding population parameter, which can arise from the sample not perfectly representing the population.

Question 4

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

Accepted Answer

While stratified random sampling can improve the precision and reduce the sampling error compared to simple random sampling, there is still potential for sampling error due to factors such as measurement error or sampling variability within strata.

Question 5

If the sampling distribution of the sample means approximates a normal distribution, then the population is normally distributed.

Accepted Answer

The statement is actually the reverse of the true relationship between the population distribution and the sampling distribution. The sampling distribution of the sample means will approach a normal distribution regardless of the population distribution, as long as the sample size is sufficiently large due to the central limit theorem. Therefore, a normal sampling distribution cannot guarantee a normal population distribution.

Question 6

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

When the sample size equals the population size, the sample is the population, so estimates of population parameters will be exact, with no sampling error.

Question 7

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 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 central limit theorem states that if the sample size, n, is sufficiently large, the sampling distribution of the means will be approximately normal, even when the population is skewed or uniform.

Accepted Answer

The statement accurately describes the central limit theorem.

Question 10

A sampling distribution of the means is a probability distribution consisting of all possible sample means of a given sample size selected from a population.

Accepted Answer

This statement is true. A sampling distribution of the means is a probability distribution that shows all the possible means of samples of a given sample size that can be selected from a population.

Question 11

If 40 samples of size 21 were selected from a population of 22,493, we would expect the mean of the sample means and the population mean to be close but not exactly equal.

Accepted Answer

This is true because the mean of the sample means (also known as the sample mean) is an unbiased estimate of the population mean, but due to sampling variability, it is unlikely to be exactly equal to the population mean. However, as the sample size increases, the sample mean becomes a more accurate estimate of the population mean.

Question 12

When doing research, knowing the population mean and other population parameters is essential.

Accepted Answer

While it can be helpful to know population parameters, it is not always essential in research. If the sample size is large enough and representative of the population, it is possible to make accurate inferences and draw conclusions without knowing the exact population parameters.

Question 13

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 systematic random sampling.

Accepted Answer

The description matches the process of systematic random sampling, where a fixed interval is used to choose participants from a population based on their order in a list.

Question 14

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

Accepted Answer

It is practically impossible to observe or study every single unit in a population due to factors such as cost, time, and resources. As a result, researchers typically study only a sample of the population to make inferences about the entire population.

Question 15

The mean of all possible sample means is equal to the population mean.

Accepted Answer

This statement is true and is known as the central limit theorem. It states that as sample size increases, the distribution of sample means approaches a normal distribution with a mean equal to the population mean.

Question 16

The central limit theorem states that for a sufficiently large sample the sampling distribution of the means of all possible samples of size n generated from the population will be approximately normally distributed with the mean of the sampling distribution equal to σ² and the variance equal to σ^2/ⁿ.

Accepted Answer

The central limit theorem states that the sampling distribution of the sample mean will be approximately normally distributed with the mean equal to the population mean (μ) and the variance equal to σ²/n, where σ² is the population variance.

Question 17

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

Accepted Answer

Sampling a population is a cost-effective way to obtain information about a population without studying every individual, which can be time-consuming and expensive.

Question 18

When deciding to collect sample information rather than collecting information from the population, the amount of time required to collect the information is unimportant.

Accepted Answer

Collecting sample information requires a smaller amount of time compared to collecting information from the entire population.

Question 19

For the sampling distribution of sample means, sampling error will decrease as sample size increases.

Accepted Answer

This is known as the central limit theorem, which states that the sampling distribution will approach a normal distribution with a smaller standard deviation (i.e. more precise estimates) as sample size increases.

Question 20

Based on the central limit theorem, the sample mean can be used as a good estimator of the population mean, assuming that the size of the sample is sufficiently large.

Accepted Answer

The answer of Based on the central limit theorem, the...

Quiz 8: Sampling Methods and the Central Limit Theorem