Deck 7: Sampling and Sampling Distributions

Question 1

Voluntary response bias occurs when the responses to questions do not reflect what the investigator had in mind.

Answer 1

False

Question 2

We can measure the accuracy of judgmental samples by applying some simple rules of probability.This way,judgmental samples are not likely to contain our built-in biases.

Answer 2

False

Question 3

An unbiased estimate is a point estimate such that the mean of its sampling distribution is equal to the true value of the population parameter being estimated.

Answer 3

True

Question 4

Stratified samples are typically not used in real applications because they provide less accurate estimates of population parameters for a given sampling cost.

Question 5

In systematic sampling,one of the first k members is selected randomly,and then every k^th member after this one is selected.The value k is called the sampling interval and equals the ratio N / n,where N is the population size and n is the desired sample size.

Question 6

Cluster sampling is often less convenient and more costly than other random sampling methods.

Question 7

In stratified sampling with proportional sample sizes,the proportion of each stratum selected differs from stratum to stratum.

Question 8

A probability sample is a sample in which the sampling units are chosen from the population by means of a random mechanism such as a random number table.

Question 9

In cluster sampling,the population is divided into subsets called clusters (such as cities or city blocks),and then a random sample of the clusters is selected.Once the clusters are selected,we typically sample all of the members in each selected cluster.

Question 10

A simple random sample is one where each member of the population has a known chance (this may differ from one member to another)or probability of being chosen.

Question 11

A list of all members of the population from which we can choose a sample is called a frame,and the potential sample members are called sampling units.

Question 12

The sampling distribution of the mean will have the same standard deviation as the original population from which the samples were drawn.

Question 13

The standard error of sample mean $x$
is large when the observations in the population are spread out (large $\sigma$
),but that the standard error can be reduced by taking a smaller sample.

Question 14

Ideally,we prefer estimates that have large standard errors.

Question 15

The size of a sample can be selected by first determining the desired standard error and then using the formula $S E ( X ) = \sigma I \sqrt { n }$
to calculate n.

Question 16

Simple random sampling can result in under-representation or over-representation of certain segments of the population.This is one of several reasons that simple random samples are almost never used in real applications.

Question 17

One obvious advantage of stratified sampling is that we obtain separate estimates within each stratum - which we would not obtain if we took a simple random sample from the entire population.A more important advantage is that we can increase the accuracy of the resulting population estimates by using appropriately defined strata.

Question 18

Simple random samples are typically used in real applications.

Question 19

The Central Limit Theorem (CLT)says that as long as the sample size is reasonably large,there is about a 95% chance that the magnitude of the sampling error for the mean will be no more than two standard errors.

Question 20

If the sample size is greater than 30,the Central Limit Theorem (CLT)will always apply.

Question 21

A point estimate is a single numeric value,a "best guess" of a population parameter,calculated from the sample data.

Question 22

An estimator is said to be unbiased if the mean of its sampling distribution equals the value of the population parameter being estimated.

Question 23

The Central Limit Theorem (CLT)states that the sampling distribution of the mean is approximately normal,no matter what the distribution of the population,so long as the sample size is large enough.

Question 24

The primary advantage of cluster sampling is sampling convenience (and possibly less cost).The downside,however,is that the inferences drawn from a cluster sample can be less accurate,for a given sample size,than for other sampling plans.

Question 25

When we sample less than 5% of the population,the finite population correction factor;fpc = $\sqrt { ( N - n ) / ( N - 1 ) }$
,is used to modify the formula for the standard error of the sample mean.

Question 26

The difference between the point estimate and the true value of the population parameter being estimated is called the estimation error.

Question 27

The standard error of an estimate is the standard deviation of the sampling distribution of the estimate.It measures how much estimates from different samples vary.

Question 28

In stratified sampling,the population is divided into relatively homogeneous subsets called strata,and then random samples are taken from each stratum.

Question 29

A confidence interval is an interval calculated from the population data,where we strongly believe the true value of the population parameter lies.

Question 30

The sampling distribution of the mean will have the same mean as the original population from which the samples were drawn.

Question 31

If a simple random sample of size n is chosen from a population of size N,then each member of the population has probability N / n of being chosen in the sample.

Question 32

Systematic sampling is generally similar to simple random sampling in its statistical properties.

Question 33

The probability of being chosen in a simple random sample of size n from a population of size N is:

A) 1/N
B) N - 1/n
C) N/n
D) n/N

Question 34

It is customary to approximate the standard error of the sample mean $\sigma / \sqrt { n }$
by substituting the sample standard deviation s for $\sigma$
in the formula: SE( $\bar { X }$
)= $\sigma / \sqrt { n }$
.

Question 35

Estimation is the process of inferring the value of an unknown population parameter using data from a random sample

Question 36

The sampling distribution of any point estimate (such as the sample mean or proportion)is the distribution of the point estimates we would obtain from all possible samples of a given size drawn from the population.

Question 37

A sample of size 20 is selected at random from a population of size N.If the finite population correction factor is 0.9418,then N must be 169.

Question 38

The averaging effect says that as you average more and more observations from a given distribution,the variance of the average increases.

Question 39

With proportional sample sizes:

A) The proportion of a stratum in the sample is independent of the proportion of that stratum in the population
B) The proportion of a stratum in the sample is the same as the proportion of that stratum in the population
C) The proportion of a stratum in the sample is greater than the proportion of that stratum in the population
D) The proportion of a stratum in the sample is less than the proportion of that stratum in the population

Question 40

The randomized response technique is a way of getting at sensitive information to avoid estimation errors due to nontruthful responses.

Question 41

The approximate standard error of the sample mean is calculated as:

A)
$\sigma I \sqrt { n }$
B)
$s I \sqrt { n }$
C)
$2 \sigma/ \sqrt { n }$
D)
$2 s / \sqrt { n }$

Question 42

A sample chosen in such a way that every possible subset of same size has an equal chance of being selected is called a(n)

A) interval estimation
B) point estimation
C) simple random sample.
D) statistic

Question 43

Which of the following is not a consideration when determining appropriate sample size?

A) The cost of sampling
B) The timely collection of the data
C) Interviewer fatigue
D) The likelihood of nonsampling error

Question 44

Identifiable subpopulations within a population are called:

A) clusters
B) samples
C) blocks
D) strata
E) None of these options

Question 45

The standard deviation of $\bar { X }$
Is usually called the

A) standard error of the mean
B) standard error of the sample
C) standard error of the population
D) randomized standard error

Question 46

The accuracy of the point estimate is measured by its:

A) standard deviation
B) standard error
C) sampling error
D) nonsampling error

Question 47

When a portion of the sample does not respond to the survey,results.

A) measurement error
B) nonresponse bias
C) sampling error
D) systematic failure
E) nonlinear error

Question 48

The approximate 95% confidence interval for a population mean is:

A)
$x \pm \sigma / \sqrt { n }$
B)
$x \pm s / \sqrt { n }$
C)
$$X \pm 2 \sigma / \sqrt { n }$$
D)
$x \pm 2 s l \sqrt { n }$

Question 49

Which of the following are reasons for why simple random sampling is used infrequently in real applications?

A) Samples can be spread over a large geographic region
B) Simple random sampling requires that all sampling units be identified prior to sampling
C) Simple random sampling can result in underrepresentation or overrepresentation of certain segments of the population
D) All of these options

Question 50

The reason the Central Limit Theorem (CLT)is such an important result in statistics is because:

A) The CLT allows us to assume that the population distribution is approximately normal,provided n is reasonably large
B) The CLT allows us to estimate the population mean without knowing the exact form of the population distribution,provided n is reasonably large
C) The CLT allows us to construct confidence intervals for the population mean without knowing the exact form of the population distribution,provided n is reasonably large
D) All of these options

Question 51

A list of all members of the population is called a:

A) sampling unit
B) probability sample
C) frame
D) relevant population

Question 52

The defining property of a simple random sample is that:

A) every sample has the same chance of being chosen
B) the easiest method to access samples are chosen
C) the fewest samples are chosen
D) every fourth subject is chosen as a sample

Question 53

The theorem that states that the sampling distribution of the sample mean $\bar { X }$
Is approximately normal when the sample size n is reasonably large is known as the:

A) central limit theorem
B) central tendency theorem
C) simple random sample theorem
D) point estimate theorem

Question 54

If systematic sampling is chosen as the sampling technique,it is probably because:

A) Systematic sampling has better statistical properties than simple random sampling
B) Systematic sampling is more convenient
C) Systematic sampling always results in more representative sampling than simple random sampling
D) None of these options

Question 55

The Central Limit Theorem (CLT)is generally valid for:

A) n > 5
B) n > 10
C) n > 20
D) n > 30
E) any size n

Question 56

A judgmental sample is a sample in which the

A) sampling units are chosen using a random number table
B) quality of sampling units judged
C) sampling units are chosen according to the sampler's judgment
D) sampling units are all biased and vocal about it

Question 57

Potential sample members,called sampling units,are:

A) people
B) companies
C) households
D) All of these options

Question 58

A sample in which the sampling units are chosen from the population by means of a random mechanism is a

A) probability sample
B) judgmental sample
C) stratified sample
D) systematic sample

Question 59

The key to using stratified sampling is:

A) identifying the strata
B) selecting the appropriate strata
C) defining the strata
D) randomizing the strata

Question 60

An unbiased estimator is a:

A) sample statistic used to approximate a population parameter
B) sample statistic,which has an expected value equal to the value of the population parameter
C) sample statistic whose value is usually less than the population parameter
D) standard error of the mean

Question 61

The mean of the sampling distribution of $$\bar { X }$$
Always equals

A) the population mean
$\mu$
B)
$\mu$ / n
C) the population standard deviation
$\sigma$
D)
$\sigma$ / n

Question 62

The opportunity for nonsampling error is increased by:

A) larger sample sizes
B) smaller sample sizes
C) affluent samples
D) educated samples

Question 63

The finite population correction factor, $\sqrt { \frac { N - n } { N - 1 } }$
,should generally be used when:

A) N is any finite size
B) n is less than 5% of the population size N
C) n is greater than 5% of the population size N
D) n is any finite size

Question 64

Selecting a random sample from each identifiable subgroup within a population is called:

A) random sampling
B) systematic sampling
C) stratified sampling
D) cluster sampling
E) None of these options

Question 65

There is approximately % chance that any particular $$\bar { X }$$
Will be within two standard deviations of the population mean ( $\mu$
))

A) 90
B) 95
C) 99
D) 99.7

Question 66

The sampling method in which a population is divided into blocks and then selected by choosing a random mechanism is called a

A) random sampling
B) systematic sampling
C) stratified sampling
D) cluster sampling

Question 67

Which of the following statements correctly describe estimation?

A) It is the process of inferring the values of known population parameters from those of unknown sample statistics.
B) It is the process of inferring the values of unknown sample statistics from those of known population parameters.
C) It is the process of inferring the values of known sample statistics from those of unknown population parameters.
D) It is the process of inferring the values of unknown population parameters from those of known sample statistics.

Question 68

Which of the following statements are correct?

A) A confidence interval describes a range of values that is likely not to include the actual population parameter
B) A confidence interval is an estimate of the range for a sample statistic.
C) A confidence interval is an estimate of the range of possible values for a population parameter.
D) None of these options

Question 69

Non-truthful response is a particular problem when:

A) sensitive questions are asked.
B) surveys are anonymous.
C) interviewers are not trained.
D) the sample is from an unusual population.

Question 70

The opportunity for sampling error is decreased by:

A) larger sample sizes
B) smaller sample sizes
C) affluent samples
D) educated samples

Question 71

Measurement error occurs when:

A) a portion of the sample does not respond to the survey
B) the sample responses are not clear
C) the responses to question do not reflect what the investigator had in mind
D) the investigator does not correctly tally all responses

Question 72

A sampling error is the result of:

A) measurement error
B) nonresponse bias
C) nontruthful responses
D) bad luck

Question 73

Which of the following statements are correct?

A) A point estimate is an estimate of the range of a population parameter
B) A point estimate is a single value estimate of the value of a population parameter
C) A point estimate is an unbiased estimator if its standard deviation is the same as the actual value of the population standard deviation
D) All of these options

Question 74

Sampling error is evident when:

A) a question is poorly worded
B) the sample is too small
C) the sample is not random
D) the sample mean differs from the population mean

Question 75

In sampling,a population is:

A) the set of all humans
B) the set of all members about which a study intends to make inferences
C) any group of test subjects
D) a random group of individuals,households,cities or countries

Question 76

The sampling mean $\bar { X }$
Is the estimate for the population mean $\mu$
)

A) random
B) point
C) simple
D) interval

Question 77

The averaging effect means that as you average more and more observations from a given distribution,the variance of the average

A) increases
B) decreases
C) is unaffected
D) could either increase,decrease or stay the same