Question 1

A convenience sample is a sample that can be easily and simply obtained with random selection.

Accepted Answer

A convenience sample is not obtained through random selection but rather consists of individuals who are easily accessible or available to the researcher. Therefore, it is not a representative sample and may not be generalizable to the larger population.

Question 2

Let  be 1 if a success occurs and 0 otherwise. Let  i.e., x is the count of the number of successes in n trials. If a random sample is taken from a population which contains only zeros and ones, the sample mean is an estimate of the actual proportion of ones in the population.

Accepted Answer

This statement is true as the sample mean, when computed, would give an estimate of the proportion of ones in the population.

Question 3

All sampling plans involve random selection of the sample from the corresponding population.

Accepted Answer

Some sampling plans, such as convenience sampling or judgmental sampling, do not require random selection. These methods select samples based on ease of access or the researcher's discretion, respectively.

Question 4

The stratified random sample is a subset of a frame, or of an associated population, chosen by randomly selecting one of the first k elements and then including every kth element thereafter until the desired sample size has been reached.

Accepted Answer

Stratified random sampling involves dividing the population into subgroups (strata) based on shared characteristics and then randomly selecting a sample from each of these groups, not by selecting every kth element.

Question 5

Which of the following is not a correct statement about the systematic random sample?

Accepted Answer

The systematic random sample is a subset of a frame or associated population chosen by randomly selecting one of the first k elements and then including every kth element hereafter until the desired sample size has been reached. Option B describes a cluster sampling technique.

Question 6

The latest U.S. census shows the population aged 25 to 40 to be 48% male and 52% female. A market research firm interested in the buying habits of young adults aged 25 to 40 instructs its interviewers to sample 300 persons, 144 of whom are to be men and 156 of whom are to be women. This is an example of a quota sample.

Accepted Answer

The description matches the definition of a quota sample, where the research firm sets specific targets or quotas for certain demographics in the sample, in this case, 48% men and 52% women.

Question 7

A questionnaire was mailed to 1000 registered municipal voters selected at random. Only 600 questionnaires were returned, and of the 600 returned, 450 respondents were strongly opposed to a surcharge proposed to support the city Parks and Recreation Department. Are you willing to accept the 75% figure as a valid estimate of the percentage in the city who are opposed to the surcharge?
______________
Why or why not?
________________________________________________________

Accepted Answer

The answer of A questionnaire was mailed to 1000 registered...

Question 8

The shape of the normal distribution is determined by its mean  and its standard deviation  .

Accepted Answer

The mean and standard deviation play a crucial role in determining the shape of the normal distribution. Specifically, the mean determines the central location of the distribution, while the standard deviation determines its spread or variability. Therefore, the statement is true.

Question 9

A 1-in-k systematic random sample involves the random selection of one of the first k elements in an ordered population, and then the systematic selection of every kth element thereafter.

Accepted Answer

This is the definition of a 1-in-k systematic random sample.

Question 10

Which of the following correctly describes a sample?

Accepted Answer

A sample is a subset of the population of interest, and its summary measures are called statistics. These summary measures, such as the sample mean, are often designated by Roman letters. Therefore, option D correctly describes a sample.

Question 11

The publisher of a newspaper decides which articles will be submitted for the consideration of the Pulitzer Prize committee. This is an example of cluster sampling.

Accepted Answer

Cluster sampling involves selecting a cluster of individuals or objects from a population, and then sampling within those clusters. In the given scenario, the publisher is not selecting a cluster and then sampling from within that cluster, but rather making a decision about which specific articles to submit for consideration. Therefore, it is not an example of cluster sampling.

Question 12

A group of people who, in response to some general appeal, have selected themselves to participate in a survey is called a simple random sample.

Accepted Answer

A simple random sample is a sample selected randomly from the population of interest, without any preference or bias towards certain individuals or groups. Therefore, it is not a group of people who have selected themselves to participate in a survey. A group of people who voluntarily choose to participate in a survey is called a voluntary response sample or a self-selected sample, which is generally not representative of the population and can lead to biased results.

Question 13

Identify the sampling design for each of the following.
The Vice President for Academic Affairs of Southern State University decides which research proposals submitted to her by each college dean will be submitted for federal funding consideration.
______________
Every student in an introductory genetics class is assigned a number. The professor then randomly selects ten numbers and surveys the corresponding students.
______________
Class rosters list student names in alphabetical order. A professor wants to select some students to participate in a research project. The professor starts with the 5th name and then selects every 10th student thereafter.
______________
An apartment complex manager randomly selects 10 buildings from the complex of 30 buildings, and then interviews one household from every apartment in the 10 buildings.
______________
The student body of a large law school is comprised of 85% in-state residents and 15% out-of-state residents. An evaluation team wishes to interview 200 alumni from the school. They are instructed to contact 170 in-state alumni and 30 out-of-state alumni.
______________

Accepted Answer

The answer of Identify the sampling design for each of...

Question 14

Quota sampling, in which the makeup of the sample must reflect the makeup of the population on some pre-selected characteristics, often has a nonrandom component in the selection process.

Accepted Answer

Quota sampling involves intentionally choosing participants to match specific characteristics of the population being studied, which involves a nonrandom component in the selection process.

Question 15

The simple random sample is a subset of a frame, or of an associated population, chosen in such a fashion that every possible subset of like size has an equal chance of being selected.

Accepted Answer

This is the definition of a simple random sample.

Question 16

Numerical descriptive measures calculated from a sample are called Statistic.

Accepted Answer

This is true. Statistic is a term used to describe numerical measures that are calculated from a sample, i.e. a portion of a larger population. These measures are used to provide information and insights about the population as a whole.

Question 17

Judgment sampling allows the sampler to decide who will or will not be included in the sample.

Accepted Answer

Judgment sampling is a non-probabilistic sampling technique in which the sampling units are selected based on the judgment of the sampler. The decision of who to include or exclude from the sample is based on the sampler's knowledge and experience, and not on a random selection process.

Question 18

Which of the following is a correct statement about the stratified random sample?

Accepted Answer

A stratified random sample is useful when the frame or population to be sampled is known to contain two or more mutually exclusive and clearly distinguishable subgroups or strata that differ greatly or are fairly homogeneous internally with respect to some characteristic of interest. This type of sample is chosen by taking separate (simple or systematic) random samples from every stratum, often in such a way that the sizes of the separate samples vary with the importance of the different strata. Therefore, all three statements in options A, B, and C are correct about a stratified random sample, making option D the correct choice.

Question 19

A list of commonly used parameters includes:

Accepted Answer

Parameters refer to population characteristics, not sample statistics. The sample mean, sample standard deviation, and sample proportion are statistics, not parameters.

Question 20

If a sample is selected at random, the main reason that the sample mean  might be different than the corresponding population mean  is that the sample might be biased.

Accepted Answer

The answer of If a sample is selected at random,...

Quiz 7: Sampling Distributions