Question 1

Results from cluster samples
A)are always representative of the population.
B)are never representative of the population.
C)should be treated with more caution than results from simple random samples.
D)should never be used to generalize to a population.

Accepted Answer

Cluster samples are a type of non-probability sampling method which can introduce bias into the sample. Therefore, the results from cluster samples should be treated with more caution than simple random samples. While they can still provide valuable insights into the population, they should not be used to generalize to the entire population.

Question 2

I use the principle of EPSEM to select a sample from my church for an opinion poll.The sample
A)is guaranteed to be representative of the population.
B)has a high probability of being representative.
C)should never be larger than 100.
D)should be larger than the population.

Accepted Answer

EPSEM (Equal Probability of Selection Method) ensures that every member of the population has an equal chance of being selected for the sample. This method does not guarantee a perfectly representative sample, but it does ensure a high probability of being representative. Therefore, choice B is the best one. Choices C and D are not accurate statements in relation to EPSEM.

Question 3

According to the theorems presented in Chapter 6,we can be sure that the sampling distribution is normal if
A)the population is small.
B)the population is normal.
C)the sample is stratified.
D)the sample is normal.

Accepted Answer

The sampling distribution will be normal if the population is normal, regardless of the sample size or sampling method.

Question 4

Cluster sampling often involves selecting
A)geographical areas.
B)systematic stratified clusters.
C)older respondents only.
D)cases alphabetically.

Accepted Answer

Cluster sampling involves grouping the population into clusters, often based on geographic areas. The clusters are then randomly selected and all individuals within the selected clusters are sampled. The other choices (B, C, and D) do not accurately describe cluster sampling methods.

Question 5

The theorems presented in Chapter 6 tell us that if a sample is "large," the sampling distribution will be
A)the same shape as the population.
B)normal.
C)small.
D)irrelevant.

Accepted Answer

The central limit theorem states that if a sample is "large" (usually n ≥ 30), the sampling distribution will be approximately normal, even if the population distribution is not normal. Therefore, choice B is the best option as it accurately reflects this concept.

Question 6

When a list of the population does not exist,the probability sampling technique most commonly used is
A)simple random.
B)stratified.
C)systematiC.
D)cluster.

Accepted Answer

Cluster sampling is often used when a complete list of the population is not available, as it involves dividing the population into clusters and then randomly selecting entire clusters for study.

Question 7

The standard deviation of the sampling distribution is represented by which of the following symbol(s)?
A)s / N
B)(s)(N)
C) $\sqrt { \sigma / N }$
D) $\sigma / \sqrt { N }$

Accepted Answer

The standard deviation of the sampling distribution is represented by the formula $\sigma / \sqrt { N }$. Option D matches this formula and is therefore the correct choice. Option A represents the standard deviation of the population, not the sampling distribution. Option B is not a valid formula for the standard deviation. Option C is close to the correct formula, but it is missing the square root around the entire fraction.

Question 8

An EPSEM sampling technique that often uses geographical areas is called
A)cluster sampling.
B)simple random sampling.
C)proportional sampling.
D)non-scientific sampling.

Accepted Answer

Cluster sampling is a type of EPSEM sampling technique in which the population is divided into clusters or groups, usually based on geographic proximity, and a random sample of clusters is selected for study. This technique is commonly used in large-scale surveys where it is not practical to sample the entire population, and is often more cost-effective and efficient than other sampling methods. Simple random sampling involves selecting individuals at random from the population, while proportional sampling involves selecting individuals based on their proportion in the population. Non-scientific sampling refers to any sampling method that does not follow standard scientific protocols. Therefore, cluster sampling is the best choice when EPSEM sampling technique often uses geographical areas.

Question 9

A properly selected cluster sample is
A)quite small.
B)non-probability.
C)EPSEM.
D)the population.

Accepted Answer

A properly selected cluster sample is EPSEM, which stands for "equal probability of selection method." This means that each cluster in the population has an equal chance of being selected for the sample. Additionally, cluster sampling is a probability sampling method, which means it involves random selection and allows for statistical inference to be made about the population. Therefore, the best choice is C.

Question 10

In a sampling distribution of sample means,most of the sample means will
A)cluster around the true population value.
B)be below the population mean in value.
C)be above the population mean in value.
D)not follow any particular pattern.

Accepted Answer

The Central Limit Theorem states that in a sampling distribution of sample means, as the sample size increases, the distribution of sample means will approach a normal distribution with the mean equal to the population mean. This means that most of the sample means will cluster around the true population value.

Question 11

With a sample size of 75,a normal sampling distribution can be assumed if
A)the cases in the sample are homogeneous.
B)the cases in the sample are heterogeneous.
C)the population distribution is normal.
D)the sample distribution is normal.

Accepted Answer

The assumption of a normal sampling distribution is based on the population distribution, not the sample itself or the homogeneity/heterogeneity of the sample. A sample size of 30 or more is typically large enough to assume a normal sampling distribution, even if the population distribution is not known or is not normal. Therefore, if the population distribution is normal, a normal sampling distribution can be assumed with a sample size of 75.

Question 12

When using systematic sampling,the researcher must
A)select only representative cases.
B)make sure that the list of the population is random or,at least,non-cyclical with respect to the variables of interest.
C)select every case.
D)select only respondents who are likely to cooperate.

Accepted Answer

Systematic sampling involves selecting every nth element from a randomly ordered list of the population. It is important to ensure that the list is random or non-cyclical with respect to the variables of interest to avoid bias in the sample. Selecting only representative cases or respondents who are likely to cooperate is not enough to ensure the sample is representative or unbiased. Selecting every case would be equivalent to a census and is not necessary for obtaining a representative sample.

Question 13

The purpose of inferential statistics is to acquire knowledge of the ____ from the ____ by means of the ____ distribution
A)population,sample,sampling
B)sample,sampling,population
C)inductive,empirical,stratified
D)theoretical,empirical,theoretical

Accepted Answer

The purpose of inferential statistics is to make inferences about the population (which is typically too large to measure directly) based on information obtained from a sample of that population. This is done by using probability theory and the sampling distribution to estimate population parameters. Therefore, Option A is the correct choice as it correctly identifies the population, sample, and sampling distribution that are essential to the process of inferential statistics.

Question 14

The mean age of all college graduates is 35.If the population distribution is normal,the mean of any sampling distribution of sample mean ages of college graduates will be
A)within plus or minus 1 standard deviation of 35.
B)close to 35.
C)35.
D)determined by the size of the distribution.

Accepted Answer

If the population distribution is normal, then the sampling distribution of sample means will also be normal. The mean of the sampling distribution of sample means will be equal to the mean of the population distribution, which is 35. Therefore, the answer is C.

Question 15

Both the sample and the population distributions are empirical,which means that they are
A)theoretical.
B)real.
C)ordinal.
D)stratifieD.

Accepted Answer

Empirical distributions are based on real data, meaning they are not theoretical. They are also not ranked or divided into strata, so options C and D can be eliminated.

Question 16

The sampling distribution links the ____ to the ____.
A)stratified,EPSEM
B)statistical,empirical
C)sample,population
D)empirical,real

Accepted Answer

The sampling distribution links the sample statistics to the population parameter.

Question 17

A sampling technique that allows you to ensure proportional representativeness in a sample is
A)representative sampling.
B)stratified sampling.
C)systematic sampling.
D)simple sampling.

Accepted Answer

Stratified sampling divides the population into relevant subgroups, or strata, and then randomly selects samples from each stratum, ensuring proportional representativeness. This technique is particularly useful when there are specific subgroups in the population that may have differing characteristics, as it allows for more accurate analysis of each group.

Question 18

A major limitation for stratified sampling is that
A)the samples so selected are not representative.
B)it violates the rule of EPSEM.
C)the samples are non-random.
D)the exact composition of the population is usually unknown.

Accepted Answer

Stratified sampling requires knowledge of the population's composition to divide it into strata, which can be challenging if the exact composition is unknown.

Question 19

Unlike the sample and population distributions,the sampling distribution is
A)empirical.
B)theoretical.
C)random.
D)EPSEM.

Accepted Answer

The sampling distribution is a theoretical distribution that represents the distribution of sample statistics (e.g., means, proportions) that would be obtained if all possible samples of a given size were taken from a population. It is not a empirical distribution, as it is not based on actual observed data. It is also not random or EPSEM, as it is determined by the population and sample design, rather than any random or equal probability selection process.

Question 20

What are the three distributions involved in every application of inferential statistics?
A)sample,sampling,and population
B)sample,stratification,cluster
C)EPSEM,random,probability
D)sampling,percentage,normal

Accepted Answer

The three distributions involved in every application of inferential statistics are sample distribution, sampling distribution, and population distribution. The sampling distribution is the distribution of a statistic based on all possible samples of the same size from the same population. The sample distribution is the distribution of a statistic for a single sample. The population distribution is the distribution of a variable for the entire population. Thus, option A is the correct answer.

Quiz 6: Introduction to Inferential Statistics: Sampling and the Sampling Distribution

Results from cluster samples

I use the principle of EPSEM to select a sample from my church for an opinion poll.The sample

According to the theorems presented in Chapter 6,we can be sure that the sampling distribution is normal if

Cluster sampling often involves selecting

The theorems presented in Chapter 6 tell us that if a sample is "large," the sampling distribution will be

When a list of the population does not exist,the probability sampling technique most commonly used is

The standard deviation of the sampling distribution is represented by which of the following symbol(s) ?

An EPSEM sampling technique that often uses geographical areas is called

A properly selected cluster sample is

In a sampling distribution of sample means,most of the sample means will

With a sample size of 75,a normal sampling distribution can be assumed if

When using systematic sampling,the researcher must

The purpose of inferential statistics is to acquire knowledge of the from the by means of the distribution

The mean age of all college graduates is 35.If the population distribution is normal,the mean of any sampling distribution of sample mean ages of college graduates will be

Both the sample and the population distributions are empirical,which means that they are

The sampling distribution links the to the .

A sampling technique that allows you to ensure proportional representativeness in a sample is

A major limitation for stratified sampling is that

Unlike the sample and population distributions,the sampling distribution is

What are the three distributions involved in every application of inferential statistics?