Deck 6: Sampling and Sampling Distributions

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.

Answer 1

every member of the population has an equal chance of being selected.

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

Answer 2

probability

Question 3

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

A)populations;samples
B)samples;populations
C)cases;samples
D)populations;datasets

Answer 3

populations;samples

Question 4

Which of the following is NOT a statistic?

A)p
B)ȳ
C)π
D)S2Y

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.

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.

Question 7

Which of the following is NOT a parameter?

A)μY
B)ȳ
C)π
D)σᵧ

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.

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.

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.

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.

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

Question 13

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

A)p
B)ȳ
C)π
D)S2Y

Question 14

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

A)μʸ
B)ȳ
C)π

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

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

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.

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

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.

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.

Question 21

The Law School Admission Test (LSAT)is designed so that test scores are normally distributed.The mean LSAT score for the population of all test-takers in 2005 was 154.35 with a standard deviation of 5.62.From Data Set 1,provide evidence that the standard error of the mean decreases as sample size increases.

Question 22

The sampling distribution is less skewed.It resembles a normal distribution.

Question 23

Disproportionate stratified sampling is especially useful when the size of some of the subgroups in the population is relatively equal.

Question 24

Will the standard error always be lower than the standard deviation? Why or why not?

Question 25

Parameter is a measure used to describe the sample distribution.

Question 26

The Law School Admission Test (LSAT)is designed so that test scores are normally distributed.The mean LSAT score for the population of all test-takers in 2005 was 154.35 with a standard deviation of 5.62.Calculate the value of the standard error of the mean for the sampling distribution for 100 samples.

Question 27

The Law School Admission Test (LSAT)is designed so that test scores are normally distributed.The mean LSAT score for the population of all test-takers in 2005 was 154.35 with a standard deviation of 5.62.If you drew all possible random samples of size 100 from the population of LSAT test-takers and plotted the values of the mean from each sample,the resulting distribution would be the sampling distribution of the mean.What is the value of the mean of the sampling distribution?

Question 28

Define systematic random sampling approach.

Question 29

In a population of 100 scores,if 20 was our sample size,then using systematic random sample,the value of K is 5.

Question 30

SELECT ALL THAT APPLY.The central limit theorem tells us that as the sample size gets larger,

A)the mean of the sampling distribution becomes equal to the population mean.
B)the standard error of the mean decreases in size.
C)the closer the sample means will be to the population mean.
D)the sample statistics clusters away from the population parameter.

Question 31

The Law School Admission Test (LSAT)is designed so that test scores are normally distributed.The mean LSAT score for the population of all test-takers in 2005 was 154.35 with a standard deviation of 5.62.From Data Set 1,if you drew all possible random samples of size 100 from the population of LSAT test-takers and plotted the values of the mean from each sample,the resulting distribution would be the sampling distribution of the mean.Would this sampling distribution be a normal distribution?

Question 32

The Law School Admission Test (LSAT)is designed so that test scores are normally distributed.The mean LSAT score for the population of all test-takers in 2005 was 154.35 with a standard deviation of 5.62.If the LSAT scores were not normally distributed,would the sampling distribution of the mean be a normal distribution if the sample size was 100?

Question 33

What is the difference between a parameter and a statistic?

Question 34

If the mean and standard deviation of a population are 436 and 103 respectively,then for a sample with a mean of 389 and a standard deviation of 96,the sampling error is 7.

Question 35

According to the central limit theorem what happens to the sampling distribution of sample means as N becomes larger?

Question 36

0,3,6,9 is a sample of the population 1,2,3,4,5,6,7,8,9,10.

Question 37

Provide the appropriate symbols for the following parameters: mean,proportion,standard deviation,and variance.

Question 38

What is the major drawback of using the proportionate stratified sample?

Question 39

A small population of N = 12 has values of 2,2,3,4,4,7,8,8,8,9,12,12.Choose ten samples of size 3 and calculate the mean and standard deviation for each.

Question 40

How is probability sampling useful?

Question 41

A small population of N = 12 has values of 2,2,3,4,4,7,8,8,8,9,12,12.Calculate the mean and standard deviation for this population.

Question 42

Consider the following population of 10 students with their corresponding test scores.

Draw a random sample of five students and find the sampling error.

Question 43

Explain the central limit theorem.

Question 44

Consider the following population of 10 students with their corresponding test scores.

Randomly draw 20 possible samples of size N = 4,and compute the mean scores for each sample.

Question 45

A small population of N = 12 has values of 2,2,3,4,4,7,8,8,8,9,12,12.Take ten samples of size 3 and calculate the mean for each.Then calculate the mean of these ten sample means.Is the mean of these sample means a good approximation of the population mean? Why or why not.

Question 46

Consider the following population of 10 students with their corresponding test scores.

Randomly draw 20 possible samples of size N = 4,and compute the mean scores for each sample.Also obtain the mean of the sampling distribution.

Question 47

If the mean and standard deviation of a population are 436 and 103 respectively,what is the standard error of the mean for a sample of size 8?

Question 48

A small population of N = 12 has values of 2,2,3,4,4,7,8,8,8,9,12,12.Choose ten samples of size 3 and calculate the mean for each.Then calculate the mean of the ten sample means.What does the mean of the ten sample means approximate in this case?

Question 49

Why is sampling distribution a theoretical distribution?

Question 50

Consider the following population of 10 students with their corresponding test scores.

Randomly draw 20 possible samples of size N = 4,and compute the mean scores for each sample.Also construct the sampling distribution of the sample means.