Question 1

When we perform ______________,an element of a population always has a chance of being chosen at each point of selection.
A)Stratified random sampling
B)Sampling with replacement
C)Sampling without replacement
D)Cluster sampling

Accepted Answer

In sampling with replacement, each element of the population can be chosen more than once, ensuring that every element always has a chance of being selected at each point of selection.

Question 2

The quantity √(N - n)(N - 1)is called the finite population multiplier.

Accepted Answer

This statement is true as the formula for the finite population multiplier is √(N - n)(N - 1) where N is the population size and n is the sample size.

Question 3

A common practice in selecting a sample from a large geographic area is multistage cluster sampling.

Accepted Answer

Multistage cluster sampling involves dividing a large geographic area into clusters and then randomly selecting smaller clusters within the larger clusters until individual participants are selected.

Question 4

The mean of the sampling distribution of $\bar { X }$ 
is always equal to the mean of the sampled population.

Accepted Answer

The central limit theorem states that as the sample size increases, the distribution of sample means approaches a normal distribution with a mean equal to the population mean. Therefore, the mean of the sampling distribution of $\bar{X}$ is always equal to the mean of the sampled population.

Question 5

A low response rate has no effect on the validity of a survey's findings.

Accepted Answer

A low response rate can lead to a biased sample and affect the representativeness of the sample, which can ultimately impact the validity of the survey's findings.

Question 6

There is no easy way to calculate an unbiased point estimate of σ.

Accepted Answer

This is true because the calculation of σ involves the use of data and the sample mean, both of which can be affected by random variation and bias, making it difficult to obtain an unbiased point estimate of σ.

Question 7

If the sample size n is infinitely large,then s² is an unbiased estimator of σ².

Accepted Answer

When the sample size is infinitely large, the sample variance (²) becomes an unbiased estimator of the population variance (σ²).

Question 8

Stratification can at times be combined with multistage cluster sampling to develop an appropriate sample.

Accepted Answer

Stratification and multistage cluster sampling are commonly used together to develop a representative sample. Stratification ensures that each subgroup in the population is represented in proportion to its size, while multistage cluster sampling allows for the selection of groups of individuals based on geographic or organizational factors. The combination of these methods can lead to a more accurate and efficient sampling process.

Question 9

The sample standard deviation s is an unbiased estimator of the population standard deviation σ.

Accepted Answer

There is no way to calculate an unbiased estimate of σ.

Question 10

Nonoverlapping groups in random sampling of a population are called:
A)Clusters.
B)A frame.
C)Strata.
D)Stages.

Accepted Answer

Strata are mutually exclusive subpopulations within a larger population. When using random sampling, it is often beneficial to divide the population into strata that are as different as possible from each other to reduce sampling error. Nonoverlapping groups are therefore called strata.

Question 11

Sampling error occurs because of incomplete information.

Accepted Answer

Sampling error occurs when incomplete information is used to draw conclusions about a population. This can result in estimates that are not representative of the true population parameters.

Question 12

The target population is the result of sampling from the original population that is of interest to the researcher.

Accepted Answer

Target population is the entire population of interest.

Question 13

The sampling distribution of the sample mean is developed by repeatedly taking samples of size n and computing the sample means and reporting the resulting sample means in the form of a probability distribution.

Accepted Answer

This is the definition of the sampling distribution of the sample mean.

Question 14

Selecting a random sample is the only way to ensure that the information reflects the true population.

Accepted Answer

Random sampling is one method to achieve a representative sample, but other methods like stratified sampling can also ensure the sample reflects the true population.

Question 15

Errors of nonobservation occur when data values are recorded incorrectly.

Accepted Answer

Errors of non-observation relate to population elements that are not observed.

Question 16

A recording error is an error of observation.

Accepted Answer

A recording error occurs when there is a mistake in the way data is gathered, documented or transcribed, which causes it to be misrepresented. It is a type of observational error.

Question 17

Methods for obtaining a sample are called:
A)Sample surveys.
B)Probability sampling.
C)Random sampling.
D)Sampling designs.

Accepted Answer

Sampling designs refer to the overall strategy or plan for selecting a sample from a population, encompassing various methods such as probability and random sampling.

Question 18

In systematic sampling,the first element is randomly selected from the first (N/n)elements.

Accepted Answer

This is the correct explanation of systematic sampling. The first element is selected randomly from the first (N/n) elements and then every (N/n)th element is selected thereafter.

Question 19

In random sampling without replacement,each element in the sample will be different.

Accepted Answer

In random sampling without replacement, once an element is selected for the sample, it is removed from the population and cannot be selected again. Therefore, each element in the sample will be different.

Question 20

Which of the following is a type of question used in survey research?
A)Dichotomous
B)Free response
C)Rating
D)All of these

Accepted Answer

All of these are types of questions used in survey research.

A) Dichotomous questions are questions that offer two options for responses (yes/no, true/false, agree/disagree).
B) Free response questions allow respondents to answer in their own words.
C) Rating questions ask respondents to rate or rank items on a scale, such as 1-5 stars or strongly agree to strongly disagree.

Quiz 7: Sampling and Sampling Distributions

When we perform ______________,an element of a population always has a chance of being chosen at each point of selection.