Chapter 6

Question 1

population

Answer 1

n A group that includes all the cases (individuals, objects, or groups) in which the researcher is
interested.

Question 2

Through the process of sampling—selecting a subset of

observations from the population—we attempt to…

Answer 2

generalize the characteristics of the larger
group (population) based on what we learn from the smaller group (the sample). This is the
basis of inferential statistics—making predictions or inferences about a population from
observations based on a sample. Thus, it is important how we select our sample

Question 3

parameter d and ex

Answer 3

The term parameter, associated with the population, refers to measures used to describe the
population we are interested in. For instance, the average commuting time for the 15,000
commuter students on your campus is a population parameter because it refers to a
population characteristic.

Question 4

In previous chapters, we have learned the many ways of
describing a distribution, such as a proportion, a mean, or a standard deviation. When used
to describe the population distribution, these measures are referred to as….

Answer 4

parameters. Thus,
a population mean, a population proportion, and a population standard deviation are all
parameters.

Question 5

We use the term statistic when referring to a c

Answer 5

a corresponding characteristic calculated for the
sample. For example, the average commuting time for a sample of commuter students is a
sample statistic. Similarly, a sample mean, a sample proportion, and a sample standard
deviation are all statistics.

Question 6

Thus, the major objective of sampling theory and

statistical inference is to provide

Answer 6

estimates of unknown parameters from sample statistics

that can be easily obtained and calculated.

Question 7

probability

Answer 7

A quantitative measure that a particular event will occur

Question 8

Probability sampling is a method that enables the researcher to s

Answer 8

specify for each case in the

population the probability of its inclusion in the sample

Question 9

The purpose of probability

sampling is to

Answer 9

select a sample that is as representative as possible of the population.

Question 10

in prob sampling, n. The

sample is selected in such a way as to allow…? what does prob sampling design let the researcher do

Answer 10

the use of the principles of probability to
evaluate the generalizations made from the sample to the population. A probability sample
design enables the researcher to estimate the extent to which the findings based on one
sample are likely to differ from what would be found by studying the entire population

Question 11

Although accurate estimates of sampling error can be made only from probability samples,
social scientists often use nonprobability samples because

Answer 11

they are more convenient and
cheaper to collect. Nonprobability samples are useful under many circumstances for a
variety of research purposes

Question 12

limitation of nonprob samples

Answer 12

Their main limitation is that they do not allow the use of the
method of inferential statistics to generalize from the sample to the population. Because
through the rest of this text we deal only with inferential statistics, we will not review
nonprobability sampling

Question 13

three sampling

designs that follow the principles of probability sampling: (

Answer 13

the simple random sample,

(2) the systematic random sample, and (3) the stratified random sample.

Question 14

Simple random sample

Answer 14

A sample designed in such a way as to ensure that (a) every member of the
population has an equal chance of being chosen and (b) every combination of N members has an equal
chance of being chosen.

Question 15

The sample is a

simple random sample because (in hospital ex)

Answer 15

every hospital had the same chance of being selected as a
member of our sample of two and (2) every combination of (N = 2) hospitals was equally
likely to be chosen.

Question 16

Systematic random sampling

Answer 16

A method of sampling in which every Kth member (K is a ratio obtained by
dividing the population size by the desired sample size) in the total population is chosen for inclusion in the
sample after the first member of the sample is selected at random from among the first K members in the
population.

Question 17

for a stratified random sample, The choice of subgroups

is based on

Answer 17

what variables are known and what variables are of interest to us.

Question 18

Stratified random sample

Answer 18

e A method of sampling obtained by (a) dividing the population into subgroups
based on one or more variables central to our analysis and (b) then drawing a simple random sample from
each of the subgroups.

Question 19

Proportionate stratified sample

Answer 19

e The size of the sample selected from each subgroup is proportional to the
size of that subgroup in the entire population.

Question 20

Disproportionate stratified sample

Answer 20

The size of the sample selected from each subgroup is disproportional
to the size of the subgroup in the population.

Question 21

Proportionate sampling can result in

Answer 21

the sample having too

few members from a small subgroup to yield reliable information about them.

Question 22

In a disproportionate stratified sample, the size of the sample selected from each subgroup

Answer 22

is deliberately made disproportional to the size of that subgroup in the population. For
instance, for our example, we could select a sample (N = 180) consisting of 90 whites
(50%), 45 blacks (25%), and 45 Latinos (25%). In such a sampling design, although the
sampling probabilities for each population member are not equal (they vary between
groups), they are known, and therefore, we can make accurate estimates of error in the
inference process.
4 Disproportionate stratified sampling is especially useful when we want
to compare subgroups with each other, and when the size of some of the subgroups in the
population is relatively small

Question 23

The sampling distribution helps estimate the

Answer 23

likelihood of our sample statistics and, therefore, enables us to generalize from the sample
to the population.

Question 24

Sampling error

Answer 24

he discrepancy between a sample estimate of a population parameter and the real
population parameter.

Question 25

Although comparing the sample estimates of the average income with the actual population
average is a perfect way to evaluate the accuracy of our estimate, in practice, we rarely have
information about

Answer 25

the actual population parameter. If we did, we would not need to
conduct a study

Question 26

This, then, is our dilemma: If sample estimates vary and if most
estimates result in some sort of sampling error,

Answer 26

how much confidence can we place in the

estimate? On what basis can we infer from the sample to the population?

Question 27

n. Because it includes all possible sample values, the sampling
distribution enables us to

Answer 27

compare our sample result with other sample values and
determine the likelihood associated with that result.
7

Question 28

Sampling distribution

Answer 28

The sampling distribution is a theoretical probability distribution of all possible
sample values for the statistics in which we are interested.

Question 29

Sampling distributions are theoretical distributions, which means that

Answer 29

hey are never really

observed.

Question 30

Constructing an actual sampling distribution would involve

Answer 30

taking all possible
random samples of a fixed size from the population. This process would be very tedious
because it would involve a very large number of samples. However, to help grasp the
concept of the sampling distribution, let’s illustrate how one could be generated from a
limited number of samples.

Question 31

Sampling distribution of the mean

Answer 31

n A theoretical probability distribution of sample means that would be
obtained by drawing from the population all possible samples of the same size.

Question 32

The Population:

Answer 32

We began with the population distribution of 20 individuals. This
distribution actually exists. It is an empirical distribution that is usually unknown to us. We
are interested in estimating the mean income for this population.

Question 33

The Sample

Answer 33

We drew a sample from that population. The sample distribution is an
empirical distribution that is known to us and is used to help us estimate the mean of the
population. We selected 50 samples of N = 3 and calculated the mean income. We
generally use the sample mean (Ῡ) as an estimate of the population mean (μ)

Question 34

The Sampling Distribution of the Mean

Answer 34

For illustration, we generated an approximation of
the sampling distribution of the mean, consisting of 50 samples of N = 3. The sampling
distribution of the mean does not really exist. It is a theoretical distribution.

Question 35

Like the population and sample distributions, the sampling distribution can be described in
terms of its m

Answer 35

mean and standard deviation. We use the symbol μῩ
to represent the mean of
the sampling distribution. The subscript indicates the specific variable of this sampling
distribution

Question 36

To obtain the mean of the sampling distribution,

Answer 36

add all the individual
sample means and divide by the number of samples (M =
50). Thus, the mean of the sampling distribution of the mean is actually the mean of
means:

Question 37

Standard error of the mean

Answer 37

The standard deviation of the sampling distribution of the mean. It describes
how much dispersion there is in the sampling distribution of the mean.

Question 38

the standard error of the mean formula tells us that

Answer 38

the standard error of the mean is equal to the standard deviation
of the population σ divided by the square root of the sample size (N).

Question 39

Third, the variability of the sampling distribution is considerably smaller than the

Answer 39

variability of the population distribution. Note that the standard deviation for the sampling
distribution ( σῩ
.= 8,480) is almost half that for the population (σ = 14,687).

Question 40

Note that as the sample size
increased, the sampling distribution became more compact. This decrease in the variability
of the sampling distribution is reflected in a smaller

Answer 40

standard deviation:

Question 41

With an increase in

sample size from N = 3 to N = 6, the standard deviation of the sampling distribution

Answer 41

decreased from 8,480 to 5,995. Furthermore, with a larger sample size, the sampling
distribution of the mean is an even better approximation of the normal curve.

Question 42

It is called the central limit theorem, and it states that i

Answer 42

if all possible random
samples of size N are drawn from a population with a mean μ and a standard deviation σ,
then as N becomes larger, the sampling distribution of sample means becomes
approximately normal, with mean μῩ
equal to the population mean and a standard
deviation equal to
( a funky formula on pg 299 if u wanna see it)))))))))))

Question 43

. Thus, the larger the sample,

Answer 43

the more closely the

sample statistic clusters around the population parameter

Question 44

Through the process of sampling, researchers attempt to

Answer 44

generalize the characteristics of a large
group (the population) from a subset (sample) selected from that group. The term parameter,
associated with the population, refers to the information we are interested in finding out. Statistic
refers to a corresponding calculated sample statistic

Question 45

A probability sample design allows us to estimate the extent to which the findings based on one
sample are likely to

Answer 45

differ from what we would find by studying the entire population.

Question 46

A simple random sample is chosen in such a way as to ensure that

Answer 46

every member of the population

and every combination of N members have an equal chance of being chosen.

Question 47

In systematic sampling

Answer 47

every Kth member in the total population is chosen for inclusion in the
sample after the first member of the sample is selected at random from the first K members in the
population.

Question 48

A stratified random sample is obtained by(2 STEPS)

Answer 48

(a) dividing the population into subgroups based on one
or more variables central to our analysis and (b) then drawing a simple random sample from each of
the subgroups

Question 49

The sampling distribution is a

Answer 49

a theoretical probability distribution of all possible sample values for
the statistic in which we are interested. The sampling distribution of the mean is a frequency
distribution of all possible sample means of the same size that can be drawn from the population of
interest

Question 50

According to the central limit theorem,

Answer 50

m, if all possible random samples of size N are drawn from a
population with a mean μ and a standard deviation σ, then as N becomes larger, the sampling
distribution of sample means becomes approximately normal, with mean μ and standard deviation

Question 51

The central limit theorem tells us that with sufficient sample size, the sampling distribution of the
mean will be

Answer 51

e normal regardless of the shape of the population distribution. Therefore, even when
the population distribution is skewed, we can still assume that the sampling distribution of the
mean is normal, given a large enough randomly selected sample size