Deck 7: Sampling and Sampling Distributions

Question 1

From a group of 12 students, we want to select a random sample of 4 students to serve on a university committee. How many different random samples of 4 students can be selected?

A) 48
B) 20,736
C) 16
D) 495

Answer 1

D

Question 2

A simple random sample from an infinite population is a sample selected such that

A) each element is selected independently and from the same population
B) each element has a 0.5 probability of being selected
C) each element has a probability of at least 0.5 of being selected
D) the probability of being selected changes

Answer 2

A

Question 3

Parameters are

A) numerical characteristics of a sample
B) numerical characteristics of a population
C) the averages taken from a sample
D) numerical characteristics of either a sample or a population

Answer 3

B

Question 4

As the sample size increases, the

A) standard deviation of the population decreases
B) population mean increases
C) standard error of the mean decreases
D) standard error of the mean increases

Question 5

Since the sample size is always smaller than the size of the population, the sample mean

A) must always be smaller than the population mean
B) must be larger than the population mean
C) must be equal to the population mean
D) can be smaller, larger, or equal to the population mean

Question 6

A population consists of 500 elements. We want to draw a simple random sample of 50 elements from this population. On the first selection, the probability of an element being selected is

A) 0.100
B) 0.010
C) 0.001
D) 0.002

Question 7

A simple random sample of 100 observations was taken from a large population. The sample mean and the standard deviation were determined to be 80 and 12 respectively. The standard error of the mean is

A) 1.20
B) 0.12
C) 8.00
D) 0.80

Question 8

In computing the standard error of the mean, the finite population correction factor is used when

A) N/n > 0.05
B) N/n ≤ 0.05
C) n/N > 0.05
D) n/N ≤ 30

Question 9

In point estimation

A) data from the population is used to estimate the population parameter
B) data from the sample is used to estimate the population parameter
C) data from the sample is used to estimate the sample statistic
D) the mean of the population equals the mean of the sample

Question 10

How many simple random samples of size 3 can be selected from a population of size 7?

A) 7
B) 21
C) 35
D) 343

Question 11

Sampling distribution of is the

A) probability distribution of the sample mean
B) probability distribution of the sample proportion
C) mean of the sample
D) mean of the population

Question 12

The probability distribution of all possible values of the sample proportion $\bar { p }$ is the

A) probability density function of $\bar { p }$
B) sampling distribution of $\bar { x }$
C) same as $\bar { p }$ , since it considers all possible values of the sample proportion
D) sampling distribution of $\bar { p }$

Question 13

The closer the sample mean is to the population mean,

A) the larger the sampling error
B) the smaller the sampling error
C) the sampling error equals 1
D) None of these alternatives is correct.

Question 14

A population has a standard deviation of 16. If a sample of size 64 is selected from this population, what is the probability that the sample mean will be within ± 2 of the population mean?

A) 0.6826
B) 0.3413
C) -0.6826
D) Since the mean is not given, there is no answer to this question.

Question 15

If we consider the simple random sampling process as an experiment, the sample mean is

A) always zero
B) always smaller than the population mean
C) a random variable
D) exactly equal to the population mean

Question 16

A population consists of 8 items. The number of different simple random samples of size 3 that can be selected from this population is

A) 24
B) 56
C) 512
D) 128

Question 17

Stratified random sampling is a method of selecting a sample in which

A) the sample is first divided into strata, and then random samples are taken from each stratum
B) various strata are selected from the sample
C) the population is first divided into strata, and then random samples are drawn from each stratum
D) None of these alternatives is correct.

Question 18

The probability distribution of the sample mean is called the

A) central probability distribution
B) sampling distribution of the mean
C) random variation
D) standard error

Question 19

Convenience sampling is an example of

A) probabilistic sampling
B) stratified sampling
C) nonprobabilistic sampling
D) cluster sampling

Question 20

Which of the following is an example of nonprobabilistic sampling?

A) simple random sampling
B) stratified simple random sampling
C) cluster sampling
D) judgment sampling

Question 21

The standard deviation of all possible values is called the

A) standard error of proportion
B) standard error of the mean
C) mean deviation
D) central variation

Question 22

The sampling error is the

A) same as the standard error of the mean
B) difference between the value of the sample mean and the value of the population mean
C) error caused by selecting a bad sample
D) standard deviation multiplied by the sample size

Question 23

A population characteristic, such as a population mean, is called

A) a statistic
B) a parameter
C) a sample
D) the mean deviation

Question 24

Which of the following sampling methods does not lead to probability samples?

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

Question 25

From a population of 200 elements, a sample of 49 elements is selected. It is determined that the sample mean is 56 and the sample standard deviation is 14. The standard error of the mean is

A) 3
B) 2
C) greater than 2
D) less than 2

Question 26

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 the

A) approximation theorem
B) normal probability theorem
C) central limit theorem
D) central normality theorem

Question 27

The sample statistic, such as , s, or , that provides the point estimate of the population parameter is known as

A) a point estimator
B) a parameter
C) a population parameter
D) a population statistic

Question 28

A probability distribution for all possible values of a sample statistic is known as

A) a sample statistic
B) a parameter
C) simple random sampling
D) a sampling distribution

Question 29

A population has a mean of 300 and a standard deviation of 18. A sample of 144 observations will be taken. The probability that the sample mean will be between 297 to 303 is

A) 0.4332
B) 0.8664
C) 0.9332
D) 0.0668

Question 30

A sample statistic, such as a sample mean, is known as

A) a statistic
B) a parameter
C) the mean deviation
D) the central limit theorem

Question 31

A single numerical value used as an estimate of a population parameter is known as

A) a parameter
B) a population parameter
C) a mean estimator
D) a point estimate

Question 32

Whenever the population has a normal probability distribution, the sampling distribution of is a normal probability distribution for

A) only large sample sizes
B) only small sample sizes
C) any sample size
D) only samples of size thirty or greater

Question 33

The standard deviation of a sample of 100 elements taken from a very large population is determined to be 60. The variance of the population

A) can not be larger than 60
B) can not be larger than 3600
C) must be at least 100
D) can be any value greater or equal to zero

Question 34

Which of the following is are) point estimators)?

A) σ
B) μ
C) s
D) α

Question 35

A population has a mean of 75 and a standard deviation of 8. A random sample of 800 is selected. The expected value of is

A) 8
B) 75
C) 800
D) None of these alternatives is correct.

Question 36

The standard deviation of a point estimator is called the

A) standard deviation
B) standard error
C) point estimator
D) variance of estimation

Question 37

The expected value of the random variable is

A) the standard error
B) the sample size
C) the size of the population
D) None of these alternatives is correct.

Question 38

The probability distribution of all possible values of the sample mean is

A) the probability density function of
B) the sampling distribution of
C) the grand mean, since it considers all possible values of the sample mean
D) one, since it considers all possible values of the sample mean

Question 39

As the sample size becomes larger, the sampling distribution of the sample mean approaches a

A) binomial distribution
B) Poisson distribution
C) normal distribution
D) chi-square distribution

Question 40

The purpose of statistical inference is to provide information about the

A) sample based upon information contained in the population
B) population based upon information contained in the sample
C) population based upon information contained in the population
D) mean of the sample based upon the mean of the population

Question 41

A simple random sample of 64 observations was taken from a large population. The sample mean and the standard deviation were determined to be 320 and 120 respectively. The standard error of the mean is

A) 1.875
B) 40
C) 5
D) 15

Question 42

A population has a mean of 53 and a standard deviation of 21. A sample of 49 observations will be taken. The probability that the sample mean will be greater than 57.95 is

A) 0
B) .0495
C) .4505
D) .9505

Question 43

The number of random samples without replacement) of size 3 that can be drawn from a population of size 5 is

A) 15
B) 10
C) 20
D) 125

Question 44

From a population of 500 elements, a sample of 225 elements is selected. It is known that the variance of the population is 900. The standard error of the mean is approximately

A) 1.1022
B) 2
C) 30
D) 1.4847

Question 45

Random samples of size 36 are taken from an infinite population whose mean and standard deviation are 20 and 15, respectively. The distribution of the population is unknown. The mean and the standard error of the mean are

A) 36 and 15
B) 20 and 15
C) 20 and 0.417
D) 20 and 2.5

Question 46

A simple random sample of 28 observations was taken from a large population. The sample mean equaled 50. Fifty is a

A) population parameter
B) biased estimate of the population mean
C) sample parameter
D) point estimate

Question 47

A sample of 400 observations will be taken from an infinite population. The population proportion equals 0.8. The probability that the sample proportion will be greater than 0.83 is

A) 0.4332
B) 0.9332
C) 0.0668
D) 0.5668

Question 48

A sample of 92 observations is taken from an infinite population. The sampling distribution of is approximately

A) normal because is always approximately normally distributed
B) normal because the sample size is small in comparison to the population size
C) normal because of the central limit theorem
D) None of these alternatives is correct.

Question 49

A population has a mean of 84 and a standard deviation of 12. A sample of 36 observations will be taken. The probability that the sample mean will be between 80.54 and 88.9 is

A) 0.0347
B) 0.7200
C) 0.9511
D) 8.3600

Question 50

Random samples of size 100 are taken from an infinite population whose population proportion is 0.2. The mean and standard deviation of the sample proportion are

A) 0.2 and .04
B) 0.2 and 0.2
C) 20 and .04
D) 20 and 0.2

Question 51

A sample of 24 observations is taken from a population that has 150 elements. The sampling distribution of is

A) approximately normal because is always approximately normally distributed
B) approximately normal because the sample size is large in comparison to the population size
C) approximately normal because of the central limit theorem
D) normal if the population is normally distributed

Question 52

There are 6 children in a family. The number of children defines a population. The number of simple random samples of size 2 without replacement) which are possible equals

A) 12
B) 15
C) 3
D) 16

Question 53

A random sample of 150 people was taken from a very large population. Ninety of the people in the sample were female. The standard error of the proportion is

A) 0.0016
B) 0.2400
C) 0.1600
D) 0.0400

Question 54

A population has a mean of 80 and a standard deviation of 7. A sample of 49 observations will be taken. The probability that the sample mean will be larger than 82 is

A) 0.5228
B) 0.9772
C) 0.4772
D) 0.0228

Question 55

For a population with any distribution, the form of the sampling distribution of the sample mean is

A) sometimes normal for all sample sizes
B) sometimes normal for large sample sizes
C) always normal for all sample sizes
D) always normal for large sample sizes

Question 56

A simple random sample of size n from an infinite population of size N is to be selected. Each possible sample should have

A) the same probability of being selected
B) a probability of 1/n of being selected
C) a probability of 1/N of being selected
D) a probability of N/n of being selected

Question 57

Random samples of size 81 are taken from an infinite population whose mean and standard deviation are 200 and 18, respectively. The distribution of the population is unknown. The mean and the standard error of the mean are

A) 200 and 18
B) 81 and 18
C) 9 and 2
D) 200 and 2

Question 58

Random samples of size 525 are taken from an infinite population whose population proportion is 0.3. The standard deviation of the sample proportions i.e., the standard error of the proportion) is

A) 0.0004
B) 0.2100
C) 0.3000
D) 0.0200

Question 59

A population has a mean of 180 and a standard deviation of 24. A sample of 64 observations will be taken. The probability that the sample mean will be between 183 and 186 is

A) 0.1359
B) 0.8185
C) 0.3413
D) 0.4772

Question 60

A simple random sample of 5 observations from a population containing 400 elements was taken, and the following values were obtained. 12 18 19 20 21
A point estimate of the mean is

A) 400
B) 18
C) 20
D) 10

Question 61

Cluster sampling is

A) a nonprobability sampling method
B) the same as convenience sampling
C) a probability sampling method
D) None of these alternatives is correct.

Question 62

The following data was collected from a simple random sample of a population. 13 15 14 16 12 The mean of the population

A) is 14
B) is 15
C) is 15.1581
D) could be any value

Question 63

The fact that the sampling distribution of sample means can be approximated by a normal probability distribution whenever the sample size is large is based on the

A) central limit theorem
B) fact that we have tables of areas for the normal distribution
C) assumption that the population has a normal distribution
D) None of these alternatives is correct.

Question 64

As a rule of thumb, the sampling distribution of the sample proportions can be approximated by a normal probability distribution whenever

A) np ≥ 5
B) n1 - p) ≥ 5 and n ≥ 30
C) n ≥ 30 and 1 - p) = 0.5
D) None of these alternatives is correct.

Question 65

Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8. The mean and the standard deviation of the sampling distribution of the sample means are

A) 8.7 and 1.94
B) 36 and 1.94
C) 36 and 1.86
D) 36 and 8

Question 66

The following data was collected from a simple random sample of a population. 13 15 14 16 12 The point estimate of the population standard deviation is

A) 2.500
B) 1.581
C) 2.000
D) 1.414

Question 67

A subset of a population selected to represent the population is

A) a subset
B) a sample
C) a small population
D) a parameter

Question 68

The following data was collected from a simple random sample of a population. 13 15 14 16 12 The point estimate of the population mean

A) cannot be determined, since the population size is unknown
B) is 14
C) is 4
D) is 5

Question 69

The sampling distribution of the sample means

A) is the probability distribution showing all possible values of the sample mean
B) is used as a point estimator of the population mean μ
C) is an unbiased estimator
D) shows the distribution of all possible values of μ

Question 70

The set of all elements of interest in a study is

A) set notation
B) a set of interest
C) a sample
D) a population

Question 71

A population of size 1,000 has a proportion of 0.5. Therefore, the proportion and the standard deviation of the sample proportion for samples of size 100 are

A) 500 and 0.047
B) 500 and 0.050
C) 0.5 and 0.047
D) 0.5 and 0.050

Question 72

The number of different simple random samples of size 5 that can be selected from a population of size 8 is

A) 40
B) 336
C) 13
D) 56

Question 73

A sample of 66 observations will be taken from an infinite population. The population proportion equals 0.12. The probability that the sample proportion will be less than 0.1768 is

A) 0.0568
B) 0.0778
C) 0.4222
D) 0.9222

Question 74

Doubling the size of the sample will

A) reduce the standard error of the mean to one-half its current value
B) reduce the standard error of the mean to approximately 70% of its current value
C) have no effect on the standard error of the mean
D) double the standard error of the mean

Question 75

A sample of 25 observations is taken from an infinite population. The sampling distribution of is

A) not normal since n < 30
B) approximately normal because is always normally distributed
C) approximately normal if np ≥ 5 and n1-P) ≥ 5
D) approximately normal if np > 30 and n1-P) > 30

Question 76

As the sample size increases, the variability among the sample means

A) increases
B) decreases
C) remains the same
D) depends upon the specific population being sampled

Question 77

A finite population correction factor is needed in computing the standard deviation of the sampling distribution of sample means

A) whenever the population is infinite
B) whenever the sample size is more than 5% of the population size
C) whenever the sample size is less than 5% of the population size
D) The correction factor is not necessary if the population has a normal distribution

Question 78

The following data was collected from a simple random sample of a population. 13 15 14 16 12 If the population consisted of 10 elements, how many different random samples of size 6 could be drawn from the population?

A) 60
B) 210
C) 3024
D) 362880

Question 79

A sample of 51 observations will be taken from an infinite population. The population proportion equals 0.85. The probability that the sample proportion will be between 0.9115 and 0.946 is

A) 0.8633
B) 0.6900
C) 0.0819
D) 0.0345

Question 80

Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8. Which of the following best describes the form of the sampling distribution of the sample mean for this situation?

A) approximately normal because the sample size is small relative to the population size
B) approximately normal because of the central limit theorem
C) exactly normal
D) None of these alternatives is correct.