Module 8

Question 1

The fundamental condition that permits proper statistical inference is
A) Random sampling
B) Normal distribution of scores
C) Knowledge of the values of the parameters of the population
D) Having a large sample

Answer 1

A) Random sampling

Question 2

Randomization and random sampling
A) Are synonymous
B) Often amount to the same thing
C) Are different procedures
D) Can be substituted for each other

Answer 2

C) Are different procedures

Question 3

In forming groups of volunteer subjects for a learning experiment, Professor Jones will most likely use
A) Randomization
B) Random sampling
C) Systematic sampling
D) Representative sampling

Answer 3

A) Randomization

Question 4

Randomization is used:
A) To select subjects randomly from a population
B) As a less complex substitute for random sampling
C) To analyze data from random samples
D) None of the above

Answer 4

D) None of the above

Question 5

Professor Smith uses flips of a coin to form two groups of 4 subjects each out of an original group of 8 subjects.  This is an example of
A) Randomization
B) Random sampling
C) Systematic sampling
D) Representative sampling

Answer 5

A) Randomization

Question 6

Which of the following is a parameter?
A) r
B) S
C) x̄
D) σ

Answer 6

D) σ

Question 7

A population characteristic is known as a
A) Element
B) Parameter
C) Statistic
D) Basic value

Answer 7

B) Parameter

Question 8

“Statistic” is to “parameter” as:
A) “Mean” is to “standard deviation”
B) “Sample” is to “population”
C) “Random sampling” is to “randomization”
D) “Calculated” is to “given”

Answer 8

B) “Sample” is to “population”

Question 9

Whether or not a sample is considered random depends on
A) The method of selection
B) How closely it resembles the population
C) Both of the above
D) None of the above

Answer 9

A) The method of selection

Question 10

Which is not a characteristic of random sampling?
A) Whether a sample is random or not cannot be told from inspection of the sample
B) Characteristics of a random sample may differ widely from characteristics of its population
C) A sample must be reasonably large to be considered a random sample
D) Every element in the population must be given an equal chance for inclusion in the sample.

Answer 10

C) A sample must be reasonably large to be considered a random sample.

Question 11

Each score in a random sampling distribution of means represents
A) A single individual
B) A random data point
C) A standard score
D) A sample mean

Answer 11

D) A sample mean

Question 12

The answer to which of the following questions is the “key” to solving a statistical inference problem?
A) Are the sample values close to the population values?
B) What sample values are likely to occur under random sampling?
C) Is the sample sufficiently representative of the population to proceed?
D) Is the sample large enough?

Answer 12

B) What sample values are likely to occur under random sampling?

Question 13

A particular sampling distribution of means is based on means of
A) All possible samples of the same size
B) n samples of the same size
C) All possible samples of all possible sizes
D) n samples of all possible sizes

Answer 13

A) All possible samples of the same size

Question 14

The correct formula for the standard error of the mean is
A) σ² / n
B) σ / n
C) √(σ / n)
D) σ / √(n)

Answer 14

D) σ / √(n)

Question 15

From the formula for the standard error of the mean, it is apparent the variation among sample means will be decreased when
A) Variation among scores in the population is less
B) Sample size is larger
C) Either (or both) of the above occurs
D) The population size is larger

Answer 15

C) Either (or both) of the above occurs

Question 16

The standard error of the mean is:
A) Given in terms of standard units
B) A standard deviation
C) Larger for larger populations
D) The average amount by which sample values are in error

Answer 16

C) A standard deviation

Question 17

The Central Limit Theorem states that
A) The mean of a sample approaches the population mean as sample size increases
B) The standard deviation of a sample approaches the population standard deviation as sample size increases
C) Sampling distributions of means tend toward normality, regardless of the shape of the population distribution
D) The limits of the central 95% of means in a sampling distribution are μ ± 1S

Answer 17

C) Sampling distributions of means tend toward normality, regardless of the shape of the population distribution

Question 18

The formula for the z ratio is similar to that for the z score.  The “score” in the formula for the z ratio is
A) x̄
B) σx̄
C) σ
D) μ

Answer 18

A) x̄

Question 19

Which is not a characteristic of the random sampling distribution of means?
A) Its mean is the same as the mean of the population of scores
B) Its standard deviation is greater than that of the population of scores
C) It tends to resemble the normal curve irrespective of the shape of the population of scores
D) Its standard deviation changes with changes in sample size

Answer 19

B) Its standard deviation is greater than that of the population of scores

Question 20

For a normal population of scores, μ = 50 and  σ = 10.  If a sample of size 100 is to be randomly selected, what is the probability of its mean falling below 51?
A) 0.9332
B) 0.6826
C) 0.9772
D) 0.8413

Answer 20

D) 0.8413

Question 21

For a normal population of scores, μ = 50 and  σ = 10. For samples of size 25, the highest 5% of sample means fall above what value?
A) 51.96
B) 51.64
C) 53.28
D) 54.31

Answer 21

C) 53.28

Question 22

A sample of size 16 is to be randomly selected from a normal population with μ = 130 and σ = 12.  What is the probability of obtaining a sample mean above 136?
A) 0.0228
B) 0.0505
C) 0.1587
D) 0.2120

Answer 22

C) 0.1587

Question 23

For a normal population of scores, μ = 130 and σ = 12. What proportion of all possible samples of size 16 will have means between 118 and 142?
A) Almost all of them
B) About two thirds of them
C) About 5% of them
D) There is insufficient information to answer

Answer 23

A) Almost all of them

Question 24

For a normal population of scores, μ = 50 and  σ = 10.  For samples of size 25, the central 95% of sample means will fall between what values (approximately)?
A) 45 and 55
B) 46 and 54
C) 40 and 50
D) 49 and 51

Answer 24

B)46 and 54

Question 25

For a normal population of scores, μ = 130 and σ = 12.  For samples of size 36, the probability of obtaining a sample mean more than 2 points away from the population mean is about:
A) 0.64
B) 0.32
C) 0.16
D) 0.10

Answer 25

B) 0.32

Question 26

The mean of the sampling distribution of means:
A) Changes as sample size is increased
B) Changes as the standard deviation of the population of scores is increased
C) Changes from μ if the population is not normally distributed
D) Is unaffected by any of the above

Answer 26

D) Is unaffected by any of the above

Question 27

A sampling distribution is a distribution of
A) Scores obtained from samples
B) Values of a statistic obtained from samples
C) Values of a parameter obtained from samples
D) Any of the above

Answer 27

B) Values of a statistic obtained from samples

Question 28

A sampling distribution is
A) A relative frequency distribution
B) A probability distribution
C) Both (A) and (B)
D) Neither (A) nor (B)

Answer 28

C) Both (A) and (B)

Question 29

The concept of random sampling distribution applies to
A) Means
B) Any measure of central tendency
C) Standard deviations
D) Any statistic

Answer 29

D) Any statistic

Question 30

The standard deviation of the sampling distribution of means:
A) Increases as sample size increases
B) Increases as the mean of the population increases
C) Increases as the standard deviation of the population decreases
D) None of the above

Answer 30

D) None of the above.