Deck 7: Sampling and Sampling Distributions

Question 1

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

A) probability density function of .
B) sampling distribution of .
C) same as , since it considers all possible values of the sample proportion.
D) sampling distribution of .

Answer 1

sampling distribution of .

Question 2

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.

Answer 2

data from the sample is used to estimate the population parameter.

Question 3

From a group of 12 students, we want to select a random sample of 5 students to serve on a university committee. How many combinations of random samples of 5 students can be selected?

A) 60
B) 95,040
C) 25
D) 792

Answer 3

792

Question 4

The sample mean is the point estimator of

A) μ.
B) σ.
C) .
D) .

Question 5

A population consists of 15 items. The number of different simple random samples of size 3 that can be selected from this population is

A) 45.
B) 455.
C) 3375.
D) 2730.

Question 6

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.

Question 7

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 8

A simple random sample of 100 observations was taken from a large population. The sample mean and the standard deviation were determined to be 1234 and 120 respectively. The standard error of the mean is

A) 1234 ± 120.
B) 120.
C) 1.2.
D) 12.

Question 9

Convenience sampling is an example of _____ sampling.

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

Question 10

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 11

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 12

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 13

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 14

The sample statistic s is the point estimator of

A) μ.
B) σ.
C) .
D) .

Question 15

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 16

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.

Question 17

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 18

How many simple random samples of size 3 can be selected from a population of size 8?

A) 336
B) 24
C) 56
D) 6561

Question 19

How many simple random samples of size 4 can be selected from a population of size 8?

A) 32
B) 4
C) 1680
D) 70

Question 20

A simple random sample of 100 observations was taken from a large population. The sample mean and the standard deviation were determined to be 50 and 5, respectively. The standard error of the mean is

A) 0.5.
B) 2.
C) 5.
D) 10.

Question 21

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

Question 22

A population has a mean of 300 and a standard deviation of 12. A sample of 64 observations will be taken. The probability that the sample mean will be between 295 to 305 is

A) 0.0009.
B) 0.9991.
C) 0.3231.
D) 0.6769.

Question 23

The standard deviation of a point estimator is called the

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

Question 24

A population has a mean of 180 and a standard deviation of 36. A sample of 84 observations will be taken. The probability that the sample mean will be between 181 and 185 is

A) 0.2980.
B) 0.7020.
C) 0.2989.
D) 0.7011.

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

Random samples of size 64 are taken from an infinite population whose mean and standard deviation are 240 and 16, respectively. The distribution of the population is unknown. The mean and the standard error of the mean are

A) 240 and 16.
B) 64 and 16.
C) 8 and 2.
D) 240 and 2.

Question 27

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

A) Binomial
B) Poisson
C) Normal
D) Chi-square

Question 28

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

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

Question 29

Which of the following is(are) point estimator(s)?

A) σ
B) μ
C) s
D) α

Question 30

A probability distribution of 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 31

Random samples of size 600 are taken from an infinite population whose population proportion is 0.4. The standard deviation of the sample proportions (i.e., the standard error of the proportion) is

A) 0.0004.
B) 0.2400.
C) 0.4000.
D) 0.0200.

Question 32

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 33

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 34

A population has a mean of 60 and a standard deviation of 18. A sample of 81 observations will be taken. The probability that the sample mean will be larger than 64 is

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

Question 35

A simple random sample of 36 observations was taken from a large population. The sample mean and the standard deviation were determined to be 360 and 120 respectively. The standard error of the mean is

A) 3.33.
B) 3.
C) 10.
D) 20.

Question 36

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 37

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 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

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

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

Question 40

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

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

Question 41

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

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

Question 42

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 43

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) irrespective of the size of the sample.

Question 44

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 standard error of the mean is

A) 24.39.
B) 28.
C) 2.
D) 1.74.

Question 45

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 0.1969 is

A) 0.0955.
B) 0.9045.
C) 0.0273.
D) 0.9727.

Question 46

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 47

A population has a mean of 125 and a standard deviation of 16. A sample of 64 observations will be taken. The probability that the sample mean will be between 122.4 and 126.1 is

A) 0.1821.
B) 0.0919.
C) 0.6120.
D) 0.3880.

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 random sample of 525 people was taken from a very large population. 225 of the people in the sample were female. The standard error of the proportion is

A) 0.9783.
B) 0.0217.
C) 0.9668.
D) 0.0332.

Question 50

Random samples of size 64 are taken from an infinite population whose mean and standard deviation are 24 and 6.4, respectively. The distribution of the population is unknown. The mean and the standard error of the mean are

A) 64 and 6.4.
B) 64 and 0.8.
C) 24 and 6.4.
D) 24 and 0.8.

Question 51

A sA 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 0.8327 and 0.8631 is

A) 0.9998.
B) 0.0002.
C) 0.2387.
D) 0.7613.

Question 52

There are 7 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) 14.
B) 21.
C) 5.
D) 42.

Question 53

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 0.75 is

A) 0.8764.
B) 0.1236.
C) 0.9938.
D) 0.0062.

Question 54

A simple random sample of 5 observations from a population containing 400 elements was taken, and the following values were obtained. 15
19
21
24
31
A point estimate of the mean is

A) 4.
B) 22.
C) 21.
D) 110.

Question 55

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 n(1-P) 5.
D) approximately normal if np > 30 and n(1-P) > 30.

Question 56

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 57

A population has a mean of 400 and a standard deviation of 25. A sample of 100 observations will be taken. The probability that the sample mean will be greater than 405 is

A) .9772.
B) .0228.
C) .4207.
D) .3805.

Question 58

Random samples of size 400 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 0.02.
C) 20 and .04.
D) 20 and 0.02.

Question 59

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

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

Question 60

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 61

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 62

The following data was collected from a simple random sample of a population. The point estimate of the population mean

A) cannot be determined, since the population size is unknown.
B) is 18.4.
C) is 18.
D) is 92.

Question 63

Four hundred people were asked whether gun laws should be more stringent. Three hundred said "yes," and 100 said "no". The point estimate of the proportion in the population who will respond "yes" is

A) 300.
B) approximately 300.
C) 0.75.
D) 0.25.

Question 64

The following information was collected from a simple random sample of a population. 9
13
15
15
21
24
The point estimate of the mean of the population is

A) 14.5.
B) 15.
C) 6.
D) 16.

Question 65

A random sample of 144 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents (i.e., of the population) is 0.3 ounces. The point estimate of the mean content of the bottles is

A) 0.3.
B) 4.
C) 144.
D) 2.

Question 66

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 67

The following data was collected from a simple random sample of a population. The point estimate of the population standard deviation is

A) 3.441.
B) 3.847.
C) 14.8.
D) 11.84.

Question 68

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 69

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.

Question 70

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

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

Question 71

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 72

Cluster sampling is

A) a nonprobability sampling method.
B) the same as convenience sampling.
C) a probability sampling method.
D) a systematic sampling method.

Question 73

A random sample of 144 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents (i.e., of the population) is 0.3 ounces. The standard error of the mean equals

A) 0.3333.
B) 0.15.
C) 0.025.
D) 4.000.

Question 74

Four hundred people were asked whether gun laws should be more stringent. Three hundred said "yes," and 100 said "no". The point estimate of the proportion in the population who will respond "no" is

A) 75.
B) 0.25.
C) 0.75.
D) 0.50.

Question 75

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

A) 2
B) 50
C) 252
D) 30,240

Question 76

The number of different simple random samples of size 5 that can be selected from a population of size 10 is

A) 50
B) 30,240
C) 2
D) 252

Question 77

The following information was collected from a simple random sample of a population. 9
13
15
15
21
24
The point estimate of the population standard deviation is

A) 7.018.
B) 59.1.
C) 7.688.
D) 49.25.

Question 78

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 79

The following data was collected from a simple random sample of a population. The mean of the population

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

Question 80

How many different samples of size 4 can be taken from a finite population of size 12?

A) 48
B) 11,880
C) 3
D) 495