Deck 7: Sampling and Sampling Distributions

Question 1

A probability sampling method in which we randomly select one of the first k elements and then select every kth element thereafter is _____.

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

Answer 1

systematic sampling

Question 2

The population being studied is usually considered ______ if it involves an ongoing process that makes listing or counting every element in the population impossible.

A) finite
B) infinite
C) skewed
D) symmetric

Answer 2

infinite

Question 3

A subset of a population selected to represent the population is a _____.

A) subset
B) sample
C) small population
D) None of the answers is correct.

Answer 3

sample

Question 4

The basis for using a normal probability distribution to approximate the sampling distribution of $\bar { x }$ and $\bar { p }$ is _____.

A) Chebyshev's theorem
B) the empirical rule
C) the central limit theorem
D) Bayes' theorem

Question 5

The standard deviation of a point estimator is the _____.

A) standard error
B) sample statistic
C) point estimate
D) sampling error

Question 6

The standard deviation of $\bar { x }$ is referred to as the _____.

A) standard x
B) standard error of the mean
C) sample standard mean
D) sample mean deviation

Question 7

The standard deviation of $\bar { p }$ is referred to as the _____.

A) standard proportion
B) sample proportion
C) average proportion
D) standard error of the proportion

Question 8

The finite correction factor should be used in the computation of $\sigma _ { \bar{x} } \text { and } \sigma _ { \bar{y} }$ when n/N is greater than _____.

A) .01
B) .025
C) .05
D) .10

Question 9

A simple random sample of size n from a finite 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 10

A population consists of 8 items. The number of different simple random samples of size 3 (without replacement) that can be selected from this population is _____.

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

Question 11

The value of the ___________ is used to estimate the value of the population parameter.

A) population statistic
B) sample parameter
C) population estimate
D) sample statistic

Question 12

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) that are possible equals _____.

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

Question 13

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 14

The expected value of $\bar { x }$ equals the mean of the population from which the sample is drawn _____.

A) only if the sample size is 30 or greater
B) only if the sample size is 50 or greater
C) only if the sample size is 100 or greater
D) for any sample size

Question 15

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 16

Excel's RAND function _____.

A) determines sample size
B) selects a simple random sample
C) randomizes a population
D) generates random numbers

Question 17

How many different samples of size 3 (without replacement) can be taken from a finite population of size 10?

A) 30
B) 1,000
C) 720
D) 120

Question 18

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) .100
B) .010
C) .001
D) .002

Question 19

A simple random sample of size n from a finite population of size N is a sample selected such that each possible sample of size _____.

A) N has the same probability of being selected
B) n has a probability of .5 of being selected
C) n has a probability of .1 of being selected
D) n has the same probability of being selected

Question 20

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 21

A sample statistic, such as $\bar { x }$ , that estimates the value of the corresponding population parameter is known as a _____.

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

Question 22

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 23

In computing the standard error of the mean, the finite population correction factor is NOT used when _____.

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

Question 24

A simple random sample of 5 observations from a population containing 400 elements was taken, and the following values were obtained. $$\begin{array} { l l l l l } 12 & 18 & 19 & 20 & 21\end{array}$$ A point estimate of the population mean is _____.

A) 5
B) 18
C) 19
D) 20

Question 25

The expected value of the random variable $\bar { x }$ is

A) ?
B) the standard error
C) the sample size
D) ?

Question 26

The sample statistic s is the point estimator of _____.

A) ?
B) ?
C) $\bar { x }$
D) $\bar { p }$

Question 27

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

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

Question 28

The standard deviation of all possible $\bar { x }$ values is called the _____.

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

Question 29

The difference between the value of the sample statistic and the value of the corresponding population parameter is called the _____.

A) statistical error
B) standard error
C) proportion error
D) sampling error

Question 30

The sample mean is the point estimator of _____.

A) ?
B) ?
C) $\bar { x }$
D) $\bar { p }$

Question 31

The sampling distribution of the sample mean _____.

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 32

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

A) parameter
B) population parameter
C) parameter or a population parameter
D) point estimate

Question 33

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 34

A numerical measure from a population, such as a population mean, is called _____.

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

Question 35

In point estimation, data from the _____.

A) population are used to estimate the population parameter
B) sample are used to estimate the population parameter
C) sample are used to estimate the sample statistic
D) None of the answers is correct.

Question 36

A simple random sample from a process (an infinite population) is a sample selected such that _____.

A) each element selected comes from the same population
B) each element is selected independently
C) each element selected comes from the same population and each element is selected independently
D) the probability of being selected changes

Question 37

The probability distribution of all possible values of the sample mean is called the ____.

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

Question 38

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) point estimator
C) sample parameter
D) point estimate

Question 39

Which of the following is a point estimator?

A) ?
B) 4
C) s
D) $\bar { x }$

Question 40

A numerical measure from a sample, such as a sample mean, is known as _____.

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

Question 41

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

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

Question 42

A sample of 24 observations is taken from a population that has 150 elements. The sampling distribution of $\bar { X }$ is _____.

A) approximately normal because $\bar { X }$ 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 43

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 mean from that sample will be larger than 82 is _____.

A) .5228
B) .9772
C) .4772
D) .0228

Question 44

From a population of 200 elements, the standard deviation is known to be 14. A sample of 49 elements is selected. It is determined that the sample mean is 56. The standard error of the mean is _____.

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

Question 45

Random samples of size 36 are taken from a process (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 distribution of sample mean are _____.

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

Question 46

For a population with an unknown distribution, the form of the sampling distribution of the sample mean is _____.

A) approximately normal for all sample sizes
B) exactly normal for large sample sizes
C) exactly normal for all sample sizes
D) approximately normal for large sample sizes

Question 47

A sample of 92 observations is taken from a process (an infinite population). The sampling distribution of $\bar { X }$ is approximately normal because _____.

A) $\bar { x }$ is always approximately normally distributed
B) the sample size is small in comparison to the population size
C) of the central limit theorem
D) None of the answers is correct.

Question 48

Whenever the population has a normal probability distribution, the sampling distribution of $\bar { X }$ 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 30 or greater

Question 49

Random samples of size 49 are taken from a population that has 200 elements, a mean of 180, and a variance of 196. The distribution of the population is unknown. The mean and the standard error of the distribution of sample means are _____.

A) 180 and 24.39
B) 180 and 28
C) 180 and 1.74
D) 180 and 2

Question 50

Random samples of size 81 are taken from a process (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 distribution of sample means are _____.

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

Question 51

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) None of the answers is correct.

Question 52

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 53

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 mean from that sample will be between 183 and 186 is _____.

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

Question 54

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

A) binomial distribution
B) Poisson distribution
C) hypergeometric distribution
D) normal probability distribution

Question 55

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 56

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 57

The fact that the sampling distribution of the sample mean 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 there are tables of areas for the normal distribution
C) assumption that the population has a normal distribution
D) normal probability theorem

Question 58

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 59

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 60

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) .0347
B) .7200
C) .9511
D) None of the answers is correct.

Question 61

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 62

Random samples of size 100 are taken from a process (an infinite population) whose population proportion is .2. The mean and standard deviation of the distribution of sample proportions are _____.

A) .2 and .04
B) .2 and .2
C) 20 and .04
D) None of the alternative answers is correct.

Question 63

All of the following are true about the standard error of the mean EXCEPT _____.

A) it is larger than the standard deviation of the population
B) it decreases as the sample size increases
C) its value is influenced by the standard deviation of the population
D) it measures the variability in sample means

Question 64

Cluster sampling is _____.

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

Question 65

The population we want to make inferences about is the _____.

A) sampled population
B) frame
C) target population
D) finite population

Question 66

A sample of 400 observations will be taken from a process (an infinite population). The population proportion equals .8. The probability that the sample proportion will be greater than 0.83 is _____.

A) .4332
B) .9332
C) .0668
D) .5668

Question 67

The standard error of the proportion will become larger as _____.

A) n increases
B) p approaches 0
C) p approaches .5
D) p approaches 1

Question 68

It is impossible to construct a frame for a(n) _____.

A) finite population
B) infinite population
C) target population
D) sampled population

Question 69

A sample of 51 observations will be taken from a process (an infinite population). The population proportion equals .85. The probability that the sample proportion will be between .9115 and .946 is _____.

A) .8633
B) .6900
C) .0819
D) .0345

Question 70

Random samples of size 525 are taken from a process (an infinite population) whose population proportion is .3. The standard deviation of the sample proportions (i.e., the standard error of the proportion) is _____.

A) .0004
B) .2100
C) .3000
D) .0200

Question 71

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

A) .0016
B) .2400
C) .1600
D) .0400

Question 72

A sample of 66 observations will be taken from a process (an infinite population). The population proportion equals .12. The probability that the sample proportion will be less than .1768 is _____.

A) .0568
B) .0778
C) .4222
D) .9222

Question 73

Which of the following is an example of a nonprobability sampling technique?

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

Question 74

A sample of 25 observations is taken from a process (an infinite population). The sampling distribution of $\bar { p }$ is _____.

A) not normal since n < 30
B) approximately normal because $\bar { p }$ is always normally distributed
C) approximately normal if np ? 5 and n(1 - p) ? 5
D) approximately normal if np > 30 and n(1 - p) > 30

Question 75

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

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

Question 76

A population of size 1,000 has a proportion of .5. Therefore, the proportion and the standard deviation of the sample proportion for samples of size 100 are _____.

A) 500 and .047
B) 500 and .050
C) .5 and .047
D) .5 and .050

Question 77

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 78

Convenience sampling is an example of _____.

A) probabilistic sampling
B) stratified sampling
C) a nonprobability sampling technique
D) cluster sampling

Question 79

When the population has a normal distribution, the sampling distribution of $X$ is normally distributed _____.

A) for any sample size
B) for any sample size of 30 or more
C) for any sample size of 50 or more
D) for any sample from a finite population

Question 80

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

A) np ≥ 5
B) n(1 − p) ≥ 5
C) n ≥ 30
D) np ≥ 5 and n(1 − p) ≥ 5