Question 1

In a simple random sample
A)every member of the population has an equal chance of being selected.
B)the population is approximately normal with the mean,median,and mode being approximately equal.
C)the mean is equal to the mode.
D)the mean of N is always equal to the standard deviation.

Accepted Answer

In a simple random sample, every member of the population has an equal chance of being selected. This is what makes it "random" and helps to ensure that the sample is representative of the population. B, C, and D are not true statements about a simple random sample.

Question 2

A method of sampling that enables researchers to specify for each case in the population the probability of its inclusion in the sample is referred to as ______ sampling.
A)inclusionary
B)case
C)probability
D)density

Accepted Answer

Probability sampling ensures that every case in the population has a known and nonzero chance of being selected for the sample, allowing researchers to generalize the sample's findings to the larger population with greater accuracy. Inclusionary and case sampling are not specific sampling methods, and density sampling is not a widely used term.

Question 3

Parameters are associated with ______;whereas,statistics are associated with ______.
A)populations;samples
B)samples;populations
C)cases;samples
D)populations;datasets

Accepted Answer

Parameters refer to characteristics of a population, while statistics refer to characteristics of a sample drawn from that population. Therefore, the correct choice is A, populations and samples.

Question 4

Which of the following is NOT a statistic?
A)p
B)ȳ
C)π
D)S2Y

Accepted Answer

"P" represents a proportion which is a statistic. "Ȳ" represents the average of a sample, also a statistic. "S2Y" represents the variance of a sample, another statistic. However, "π" represents the mathematical constant pi, which is not a statistic.

Question 5

If all possible random samples of size N are drawn from a population with a mean of μY and a standard deviation of óᵧ,then as N becomes larger,the sampling distribution of sample means becomes approximately normal with a mean of and a standard deviation of ó?.This statement is known as the
A)sampling frame.
B)sampling distribution.
C)central sampling theorem.
D)central limit theorem.

Accepted Answer

This statement is known as the central limit theorem, which states that as the sample size (N) becomes larger, the sampling distribution of sample means becomes approximately normal with a mean of μY and a standard deviation of óᵧ divided by the square root of N (represented by ó?). The central limit theorem is a fundamental concept in statistics and is widely used in hypothesis testing, confidence intervals, and other statistical analyses.

Question 6

SELECT ALL THAT APPLY.
-Probability
A)can be expressed as a proportion.
B)can be expressed as a percentage.
C)can take a maximum value of 1.
D)can take a minimum value of 1.

Accepted Answer

A) Probability can be expressed as a proportion, such as 0.5 or 1/2.
B) Probability can also be expressed as a percentage, such as 50% or 1/2(100%).
C) Probability always ranges from 0 to 1, so its maximum value can be 1. It cannot be greater than 1 because it represents the likelihood of an event occurring, and if the likelihood is more than 100%, it is impossible. 
D) Probability cannot take a minimum value of 1 as it always ranges between 0 to 1.

Question 7

Which of the following is NOT a parameter?
A)μY
B)ȳ
C)π
D)σᵧ

Accepted Answer

B) ȳ represents a sample mean, which is a statistic, not a parameter. Parameters describe populations, while statistics describe samples.

Question 8

A relatively small subset from a group that includes all of the cases that a researcher is interested is referred to as a
A)sample.
B)population.
C)case.
D)dataset.

Accepted Answer

A sample is a smaller group selected from a larger group or population that a researcher is interested in studying. This allows the researcher to make inferences about the larger population based on the characteristics and behaviors of the sample group. Therefore, a sample is the best choice for this scenario.

Question 9

A group that includes all the cases in which a researcher is interested is referred to as a
A)sample.
B)population.
C)case.
D)dataset.

Accepted Answer

A population refers to the entire group that a researcher is interested in studying, whereas a sample is a smaller subset of that group that is actually studied. Choice A (sample) is incorrect because it is not the larger group that a researcher is interested in studying. Choice C (case) is incorrect because it refers to a single individual or unit being studied, not the entire group. Choice D (dataset) is incorrect because it refers to a collection of data rather than a group of individuals or units being studied.

Question 10

SELECT ALL THAT APPLY.
-In a population of 250 students,60% are Whites,20% are Latinos,15% are Blacks,and 5% others.In a proportionate stratified random sample of 120,
A)the number of Whites selected is 72.
B)the number of Blacks selected is 50.
C)the number of Latinos selected is 37.
D)the number of other racial and ethnicity background selected is 6.

Accepted Answer

- A: 60% of 250 is 150. 150 out of 250 is the same proportion as 72 out of 120, so 72 Whites are selected.- D: 5% of 250 is 12.5, rounding to the nearest whole number gives 12 or 13, but since we're working with a sample of 120, 5% of 120 is exactly 6, matching the proportion in the population.

Question 11

When the size of the sample selected from a subgroup is proportional to the size of the that subgroup in the entire population,we refer to this as
A)systematic random sampling.
B)proportionate stratified sampling.
C)stratified cluster sampling.
D)disproportionate stratified sampling.

Accepted Answer

Proportionate stratified sampling involves selecting a sample proportionally from each stratum based on the size of the stratum in the entire population. This ensures that each stratum is represented adequately in the sample, and provides more accurate estimates for the population as a whole. Systematic random sampling involves selecting every nth individual from a list or population, while stratified cluster sampling involves dividing the population into clusters and randomly selecting clusters to sample from. Disproportionate stratified sampling involves selecting different sample sizes from each stratum, which can lead to biased estimates if not properly accounted for.

Question 12

______ is necessary because researchers in the social sciences almost never have enough resources to collect information about the entire set of subjects of interest to them.
A)Central tendency
B)Variability
C)Sampling
D)Statistical analysis

Accepted Answer

Sampling is necessary because it allows researchers to select a smaller subset of subjects from the larger population of interest, which saves time and resources while still allowing for the generalization of findings to the entire population. Central tendency (A) and variability (B) are concepts related to the measurement of characteristics within a sample or population, while statistical analysis (D) is a broader term that encompasses a range of methods used to analyze data.

Question 13

Which of the following is the notation for the sample mean?
A)p
B)ȳ
C)π
D)S2Y

Accepted Answer

The notation for sample mean is usually ȳ (pronounced y-bar). Option A is the notation for proportion in statistics. Option C is the Greek letter used to represent pi (π) in math. Option D is the notation for the sample variance.

Question 14

Which of the following is the notation for the population mean?
A)μʸ
B)ȳ
C)π

Accepted Answer

μ is the symbol for population mean in statistics.

Question 15

Which of the following two qualities are used to calculate the standard error of the mean?
A)Sample mean and population mean
B)Sample mean and sample standard deviation
C)Population standard deviation and sample size
D)Population standard deviation and sample mean

Accepted Answer

The standard error of the mean is calculated using the population standard deviation divided by the square root of the sample size.

Question 16

Which of the following sampling approaches first divides the population into subgroups based on one or more variables of interest?
A)Simple statistical sampling
B)Systematic random sampling
C)Stratified random sampling
D)Systematic density sampling

Accepted Answer

Stratified random sampling first divides the population into subgroups based on one or more variables of interest, and then randomly selects participants from each subgroup to ensure representation from all subgroups in the sample. Simple statistical sampling does not involve subgroups, systematic random sampling selects every nth participant, and systematic density sampling involves selecting participants based on their spatial proximity.

Question 17

SELECT ALL THAT APPLY.
-The probability of rolling an even number with a six-sided,equally weighted die is
A)1/3.
B)1/2.
C)1/6.
D)3/6.

Accepted Answer

- B) The probability of rolling an even number can be calculated as the number of even outcomes (2, 4, or 6) divided by the total number of possible outcomes (1, 2, 3, 4, 5, or 6). This gives us a probability of 3/6 or 1/2.
- D) This is also a correct choice as it represents the same probability as choice B, i.e., 3/6 or 1/2, but it's not the best choice as it doesn't give an explicit answer.

Question 18

What is sampling error?
A)The discrepancy between the sample mean and the sample standard deviation
B)The discrepancy between the observed mean of one group in the sample and the observed mean of another group in the sample
C)The discrepancy between a sample estimate of a population parameter and the real population parameter
D)The discrepancy between two population parameters of interest

Accepted Answer

Sampling error refers to the discrepancy between a sample estimate of a population parameter and the real population parameter. It is caused by the fact that a sample is only a subset of the population, and therefore may not perfectly represent the true characteristics of the population.

Question 19

SELECT ALL THAT APPLY.
-In a simple random sample
A)the population is divided into subgroups based on one or more variables.
B)K = population size/sample size.
C)every member of the population has an equal chance of being chosen.
D)every combination of N members has an equal chance of being chosen.

Accepted Answer

C) In a simple random sample, every member of the population indeed has an equal chance of being selected, ensuring that the sample is representative of the population.D) Additionally, in a simple random sample, every possible combination of N members (where N is the sample size) has an equal chance of being chosen, which is a defining characteristic of this sampling method.

Question 20

A theoretical probability distribution of all possible sample values for the statistics in which we are interested in is referred to as a
A)sample.
B)sampling distribution.
C)population.
D)sampling frequency.

Accepted Answer

A sampling distribution is the theoretical probability distribution of all possible sample values for the statistics in which we are interested in. This distribution helps us understand the characteristics of the sampling process and the behavior of the statistics we estimate from the samples. A sample is a set of observations drawn from the population, while the population is the entire group of individuals, objects, or events we want to study. Sampling frequency is not a commonly used term in statistical inference.

Quiz 6: Sampling and Sampling Distributions

In a simple random sample

A method of sampling that enables researchers to specify for each case in the population the probability of its inclusion in the sample is referred to as ______ sampling.

Parameters are associated with ;whereas,statistics are associated with .

Which of the following is NOT a statistic?

If all possible random samples of size N are drawn from a population with a mean of μY and a standard deviation of óᵧ,then as N becomes larger,the sampling distribution of sample means becomes approximately normal with a mean of and a standard deviation of ó?.This statement is known as the

SELECT ALL THAT APPLY. -Probability

Which of the following is NOT a parameter?

A relatively small subset from a group that includes all of the cases that a researcher is interested is referred to as a

A group that includes all the cases in which a researcher is interested is referred to as a

SELECT ALL THAT APPLY. -In a population of 250 students,60% are Whites,20% are Latinos,15% are Blacks,and 5% others.In a proportionate stratified random sample of 120,

When the size of the sample selected from a subgroup is proportional to the size of the that subgroup in the entire population,we refer to this as

______ is necessary because researchers in the social sciences almost never have enough resources to collect information about the entire set of subjects of interest to them.

Which of the following is the notation for the sample mean?

Which of the following is the notation for the population mean?

Which of the following two qualities are used to calculate the standard error of the mean?

Which of the following sampling approaches first divides the population into subgroups based on one or more variables of interest?

SELECT ALL THAT APPLY. -The probability of rolling an even number with a six-sided,equally weighted die is

What is sampling error?

SELECT ALL THAT APPLY. -In a simple random sample

A theoretical probability distribution of all possible sample values for the statistics in which we are interested in is referred to as a