Deck 7: Sampling and Sampling Distributions

Question 1

We can randomly select a sample from an infinite population of potential process measurements by sampling the process at different and equally spaced time points.

Answer 1

True

Question 2

If a population is known to be normally distributed,then it follows that the sample mean must equal the population mean.

Answer 2

False

Question 3

If the sampled population distribution is skewed,then in most cases the sampling distribution of the mean can be approximated by the normal distribution if the sample size n is at least 30.

Answer 3

True

Question 4

If a population is known to be normally distributed,then it follows that the sample standard deviation must equal σ.

Question 5

The sampling distribution of must be a normal distribution with mean = 0 and standard deviation = 1.

Question 6

If the sampled population is exactly normally distributed,then the sampling distribution of is also expected to be normal,regardless of the sample size.

Question 7

A sample size of 500 is sufficiently large to conclude that the sampling distribution of is a normal distribution,when the estimate of the population proportion is .995.

Question 8

The standard deviation of all possible sample proportions increases as the sample size increases.

Question 9

If p = .9 and n = 40,then we can conclude that the sampling distribution of is approximately a normal distribution.

Question 10

The Central Limit Theorem states that as sample size increases,the population distribution more closely approximates a normal distribution.

Question 11

A minimum variance,unbiased point estimate has a variance that is as small as or smaller than the variances of any other unbiased point estimate.

Question 12

The reason sample variance has a divisor of n - 1 rather than n is that it makes the variance an unbiased estimate of the population variance.

Question 13

A sample statistic is an unbiased point estimate of a population parameter if the mean of the populations of all possible values of the sample statistic equals the population parameter.

Question 14

For any sampled population,the population of all sample means is approximately normally distributed.

Question 15

The standard deviation of the sampling distribution of the sample mean is σ.

Question 16

If p = .8 and n = 50,then we can conclude that the sampling distribution of is approximately a normal distribution.

Question 17

If we have a sample size of 100 and the estimate of the population proportion is .10,we can estimate the sampling distribution of with a normal distribution.

Question 18

In order to select a stratified random sample,we divide the population into overlapping groups of similar elements.

Question 19

As the sample size increases,the standard deviation of the sampling distribution increases.

Question 20

The sampling distribution of a sample statistic is the probability distribution of the population of all possible values of the sample statistic.

Question 21

A recording error is an error of observation.

Question 22

Stratification can at times be combined with multistage cluster sampling to develop an appropriate sample.

Question 23

In systematic sampling,the first element is randomly selected from the first (N/n)elements.

Question 24

Errors of nonobservation occur when data values are recorded incorrectly.

Question 25

There is no easy way to calculate an unbiased point estimate of σ.

Question 26

Sampling error occurs because of incomplete information.

Question 27

If the sample size n is infinitely large,then s² is an unbiased estimator of σ².

Question 28

Selecting a random sample is the only way to ensure that the information reflects the true population.

Question 29

Nonoverlapping groups in random sampling of a population are called:

A)Clusters.
B)A frame.
C)Strata.
D)Stages.

Question 30

The target population is the result of sampling from the original population that is of interest to the researcher.

Question 31

A low response rate has no effect on the validity of the findings from a survey.

Question 32

In random sampling without replacement,each element in the sample will be different.

Question 33

The sample standard deviation s is an unbiased estimator of the population standard deviation σ.

Question 34

When we perform ______________,an element of a population always has a chance of being chosen at each point of selection.

A)Stratified random sampling
B)Sampling with replacement
C)Sampling without replacement
D)Cluster sampling

Question 35

A common practice in selecting a sample from a large geographic area is multistage cluster sampling.

Question 36

The quantity √[(N - n)(N - 1)] is called the finite population multiplier.

Question 37

Which of the following is a type of question used in survey research?

A)Dichotomous
B)Free response
C)Rating
D)All of these

Question 38

The sampling distribution of the sample mean is developed by repeatedly taking samples of size n and computing the sample means and reporting the resulting sample means in the form of a probability distribution.

Question 39

The mean of the sampling distribution of is always equal to the mean of the sampled population.

Question 40

Methods for obtaining a sample are called:

A)Sample surveys.
B)Probability sampling.
C)Random sampling.
D)Sampling designs.

Question 41

_____________ is the difference between a numerical description of the population and the corresponding descriptor of the sample.

A)Sampling error
B)Nonobservation error
C)Observation error
D)Nonresponse

Question 42

____________ says that if the sample size is sufficiently large,then the sample means are approximately normally distributed.

A)Cluster sampling
B)Sampling error
C)Sampling distribution of the mean
D)The Central Limit Theorem

Question 43

Whenever the population has a normal distribution,the sampling distribution of is normal or near normal distribution:

A)For only large sample sizes.
B)For only small sample sizes.
C)For any sample size.
D)For only samples of size 30 or more.

Question 44

The spread of the sampling distribution of is ____________ the spread of the corresponding population distribution sampling distribution.

A)Larger than
B)Smaller than
C)The same as
D)Exactly ½

Question 45

If a population distribution is known to be normal,then it follows that:

A)The sample mean must equal the population mean.
B)The sample mean must equal the population mean for large samples.
C)The sample standard deviation must equal the population standard deviation.
D)All of these.
E)None of these.

Question 46

If the sampled population has a mean of 48 and standard deviation of 16,then the mean and the standard deviation for the sampling distribution of for n = 16 are:

A)4 and 1.
B)12 and 4.
C)48 and 4.
D)48 and 1.
E)48 and 16.

Question 47

The mean of the sampling distribution of the sample proportion is equal to _____ when the sample size is sufficiently large.

A)μ
B)p
C)p × n
D)(1 - p)

Question 48

The Central Limit Theorem states that as the sample size increases,the distribution of the sample ____________ approaches the normal distribution.

A)Medians
B)Means
C)Standard deviations
D)Variances

Question 49

Consider a sampling distribution formed based on n = 3.The standard deviation of the population of all sample means is ______________ less than the standard deviation of the population of individual measurements σ.

A)Always
B)Sometimes
C)Never

Question 50

For nonnormal populations,as the sample size (n)___________________,the distribution of sample means approaches a(n)________________ distribution.

A)Decreases;uniform
B)Increases;normal
C)Decreases;normal
D)Increases;uniform
E)Increases;exponential

Question 51

As the sample size ______________,the variation of the sampling distribution of ___________.

A)Decreases,decreases
B)Increases,remains the same
C)Decreases,remains the same
D)Increases,decreases
E)None of these

Question 52

The notation for the standard deviation of the sampling distribution of the sample mean is __________.

A)
B)σx
C)
D)μ

Question 53

If the sampled population is finite and at least _____ times larger than the sample size,we treat the population as infinite.

A)5
B)20
C)30
D)10

Question 54

According to the Central Limit Theorem,if a sample size is at least _____,then for most sampled populations,we can conclude that the sample means are approximately normal.

A)25
B)20
C)30
D)50

Question 55

__________ sampling is defined as sampling where we know the chance that each element in the population will be included in the sample.

A)Judgment
B)Convenience
C)Nonrandom
D)Probability

Question 56

_____________ occurs when some population elements are excluded from the process of selecting the sample.

A)Nonresponse
B)An error of observation
C)Undercoverage
D)Sampling error

Question 57

If we wish to estimate a population parameter by using a sample statistic,we are using ___________.

A)Cluster sampling
B)Point estimation
C)Random sampling
D)Response bias

Question 58

For large samples,the sampling distribution of is approximately normal with a mean of _____.

A)μ
B)μ/√n
C)
D)z

Question 59

The population of all sample proportions has a normal distribution if the sample size (n)is sufficiently large.The rule of thumb for ensuring that n is sufficiently large is:

A)np ≥ 5
B)n(1 - p)≥ 5
C)np ≤ 5
D)n(1 - p)≤ 5 and np ≤ 5
E)np ≥ 5 and n(1 - p)≥ 5

Question 60

A Yes or No question is _____________.

A)Dichotomous
B)Multiple choice
C)Open-ended
D)Systematic

Question 61

As the sample size increases,the variability of the sampling distribution of the mean ______________.

A)Increases
B)Stays the same
C)Is variable
D)Decreases

Question 62

A random sample of size 1,000 is taken from a population where p = .20.Describe the sampling distribution of .

A)Cannot be determined
B)Approximately normal
C)Skewed to the left
D)Skewed to the right

Question 63

Find P( < 402),if μ = 400,σ_x = 200,and n = 100.

A).8413
B).4602
C).5398
D).1587

Question 64

Find σ_x,if μ = 400,P( < 396)= .0228,and n = 100.

A)0.20
B)200
C)20
D)2.00

Question 65

A PGA (Professional Golf Association)tournament organizer is attempting to determine whether hole (pin)placement has a significant impact on the average number of strokes for the 13^th hole on a given golf course.Historically,the pin has been placed in the front right corner of the green,and the historical mean number of strokes for the hole has been 4.25,with a standard deviation of 1.6 strokes.On a particular day during the most recent golf tournament,the organizer placed the hole (pin)in the back left corner of the green.64 golfers played the hole with the new placement on that day.Determine the probability of the sample average number of strokes exceeding 4.75.

A).9938
B).4013
C).0062
D).3783

Question 66

Find P( < 25)if μ = 16 and = 4.

A)1.000
B)2.25
C).9878
D).0122

Question 67

Find P(395.4 < < 404.6),if the population mean = 400,σ_x = 20,and n = 100.

A).9786
B).9999
C).0214
D).9893

Question 68

An unbiased estimate of σ² is _____.

A)s
B)s²
C)
D)σ

Question 69

A random sample of size 36 is taken from a population with a mean of 50 and a standard deviation of 5.The sampling distribution of ____________________.

A)Cannot be determined
B)Is skewed to the left
C)Is approximately normal
D)Is skewed to the right

Question 70

The ___________ is a minimum-variance unbiased point estimate of the mean of a normally distributed population.

A)Sample mean
B)Sample variance
C)Sample standard deviation
D)Observed mean

Question 71

As the sample size ___________,the standard deviation of the population of all sample proportions increases.

A)Increases
B)Stays the same
C)Is variable
D)Decreases

Question 72

The sampling distribution of the sample mean is a normal distribution for ________ sample sizes,regardless of the shape of the corresponding population distribution.

A)Random
B)Large
C)Larger than 50
D)Small

Question 73

Packages of sugar bags for Sweeter Sugar Inc.have an average weight of 16 ounces and a standard deviation of 0.2 ounces.The weights of the sugar packages are normally distributed.What is the probability that 16 randomly selected packages will have a weight in excess of 16.075 ounces?

A).0500
B).3520
C).9332
D).0668

Question 74

The ______________ of a sample statistic is the probability distribution of the population of all possible values of the sample statistic.

A)Sample mean
B)Sampling Distribution of Sample Mean
C)Probability
D)Observations

Question 75

The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.3 inches.What is the probability that the average length of a steel sheet from a sample of 9 units is more than 29.95 inches long?

A).8413
B).6293
C).3707
D).1587

Question 76

Find P( > 2,510)if μ = 2,500 and = 7.

A).0764
B).9998
C).9236
D).0001

Question 77

The population of all _________________ proportions is described by the sampling distribution of .

A)Population
B)Random
C)Observed
D)Sample

Question 78

Find P( > 172),if μ = 175 and = 9.

A).1587
B).8413
C).6293
D).3707

Question 79

A theorem that allows us to use the normal probability distribution to approximate the sampling distribution of sample means and sample proportions whenever the sample size is large is known as _______________.

A)Cluster sampling
B)Sampling error
C)Sampling distribution of the mean
D)The Central Limit Theorem

Question 80

Find P( < 35)if μ = 40,σ_x = 16,n = 16.

A).9944
B).4483
C).5517
D).1056