Question 1

Which of the following statements about cluster sampling is false?​

Accepted Answer

A)  ​All elements within the randomly selected clusters form the sample 
B)  ​It generally requires a smaller total sample size than simple random sampling 
C)  ​Ideally, each cluster is a representative small-scale version of the entire population 
D)  ​It provides the best results when the elements within the clusters are not alike 
A)  ​All elements within the randomly selected clusters form the sample 
B)  ​It generally requires a smaller total sample size than simple random sampling 
C)  ​Ideally, each cluster is a representative small-scale version of the entire population 
D)  ​It provides the best results when the elements within the clusters are not alike B

Question 2

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

Accepted Answer

A)  not normal since n  30 and n(1-P) > 30. 
A)  not normal since n  30 and n(1-P) > 30. C

Question 3

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

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

The desired situation is when the sampled population is _____ the targeted population.

Accepted Answer

A)  identical to 
B)  larger than 
C)  smaller than 
D)  more varied than 
A)  identical to 
B)  larger than 
C)  smaller than 
D)  more varied than

Question 6

The absolute value of the difference between the point estimate and the population parameter it estimates is the _____ error.

Accepted Answer

A)  standard 
B)  sampling 
C)  efficient 
D)  finite 
A)  standard 
B)  sampling 
C)  efficient 
D)  finite

Question 7

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

Accepted Answer

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

Question 8

Cluster sampling is

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

Nonsampling error that results when the incorrect measurement of the population characteristic of interest is which of the following?

Accepted Answer

A)  Coverage error 
B)  Nonresponse error 
C)  Measurement error 
D)  Research error 
A)  Coverage error 
B)  Nonresponse error 
C)  Measurement error 
D)  Research error

Question 11

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

Accepted Answer

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

Question 12

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

Accepted Answer

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. 
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 13

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.

Accepted Answer

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

Question 14

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

Accepted Answer

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. 
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 15

The sample mean is the point estimator of

Accepted Answer

A)  μ. 
B)  σ. 
C)    . 
D)    . 
A)  μ. 
B)  σ. 
C)    . 
D)    .

Question 16

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

Accepted Answer

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

Question 17

The standard deviation of   is referred to as the​

Accepted Answer

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

Question 18

Sampling distribution of   is the

Accepted Answer

A)  probability distribution of the sample mean. 
B)  probability distribution of the sample proportion. 
C)  mean of the sample. 
D)  mean of the population. 
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 19

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

Accepted Answer

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

Question 20

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

Accepted Answer

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. 
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.

Exam 7: Sampling and Sampling Distributions

Which of the following statements about cluster sampling is false?​

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

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 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

The desired situation is when the sampled population is _____ the targeted population.

The absolute value of the difference between the point estimate and the population parameter it estimates is the _____ error.

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

Cluster sampling is

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

Nonsampling error that results when the incorrect measurement of the population characteristic of interest is which of the following?

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

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.

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

The sample mean is the point estimator of

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

The standard deviation of is referred to as the​

Sampling distribution of is the

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

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

Data and Statistics

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Introduction to Probability

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Which of the following statements about cluster sampling is false?

The standard deviation of is referred to as the