Deck 7: Sampling Distribution of Means

Question 1

The sampling distribution of means is

A) an empirical distribution.
B) based on all possible populations.
C) a theoretical distribution.
D) based on the mean calculated for our current sample.

Answer 1

C

Question 2

The central limit theorem covers all of the following aspects of the sampling distribution of means, except the

A) standard deviation.
B) shape.
C) mean.
D) stability of the deviation scores.

Answer 2

D

Question 3

The shape, mean, and standard deviation of the sampling distribution of means are all discussed in the

A) central limit theorem.
B) Pythagorean theorem.
C) trichotomy theorem.
D) Poisson limit theorem.

Answer 3

A

Question 4

According to the central limit theorem, the mean of the sampling distribution of means will equal _______.

A) M
B) μ
C) 0
D) 1

Question 5

Which of the following statements is true regarding the sampling distribution of means?

A) If the population from which a sample was drawn is not normal, then the sampling distribution cannot be normal.
B) If the sample drawn from the population is small enough, then the sampling distribution can be normal, even if the population itself is not.
C) If the sample drawn from the population is large enough, then the sampling distribution can be normal, even if the population itself is not.
D) None of the above statements is true.

Question 6

The mean of the sampling distribution of means is called the _________________.

A) expected value
B) standard error of the mean
C) grand mean
D) overall mean

Question 7

The symbol that represents the expected value of a sampling distribution of means is _____.

A) M
B) μ
C) μ_M
D) σ_M

Question 8

If we added up all of our means from a sampling distribution of means and divided by the number that represented all possible samples, the result would be the _______________.

A) standard error of the mean
B) grand mean
C) expected value
D) overall mean

Question 9

Given a population mean of 68 and a standard deviation of 6, the sampling distribution of means will have an expected value of __________.

A) M
B) 6
C) 68
D) More information is needed to make this determination.

Question 10

The amount that a sample mean is expected to vary from the population mean is given by the ________________.

A) average deviation
B) grand mean
C) expected value
D) standard error of the mean

Question 11

The symbol that represents the standard error of the mean is _______.

A) σ_M
B) M_σ
C) μ_σ
D) σ_μ

Question 12

The standard error of the mean is based on the

A) standard deviation and the mean of a sample.
B) mean and the size of the sample.
C) standard deviation and the size of the sample.
D) shape of the distribution.

Question 13

Given the same value for the standard deviation from two distributions but different sample sizes,

A) the smaller sample will more accurately predict the population mean.
B) the amount of standard error will be the same for both distributions.
C) the smaller sample will produce less standard error.
D) the larger sample will produce less standard error.

Question 14

Given the same standard deviation for two different distributions, as the size of the sample decreases

A) the expected value increases.
B) the expected value also decreases.
C) the size of the standard error also decreases.
D) the size of the standard error increases.

Question 15

Given μ = 75 and a σ = 10, the expected value for a sampling distribution of means, based on sample sizes of 36, will be _______.

A) 75
B) 2.08
C) 10
D) 12.5

Question 16

A sample of n = 25 is selected at random from a population with a σ = 15. Approximately how much difference in the scores would you expect between the sample mean and the population mean?

A) 15 points
B) 1.67 points
C) 3 points
D) .6 point

Question 17

In order to determine the standard error of the mean, we need to know

A) μ and σ.
B) σ and n.
C) M and σ.
D) μ and n.

Question 18

Given n = 9 and σ_M = 12, what is σ?

A) 3
B) 1.33
C) .75
D) 36

Question 19

The standard deviation for two different distributions is 12. The sample size for one of the distributions is 36. Which of the following sample sizes for the other distribution will produce the greatest amount of standard error?

A) 49
B) 64
C) 81
D) Not enough information is provided to make the determination.

Question 20

The mean for a set of scores is 52, the standard deviation is 14, and the sample size is 36. What is the standard error of the mean?

A) 1.14
B) 2.33
C) .39
D) 1.45

Question 21

The standard deviation for a set of scores is 10 and the sample size is 42. What is the standard error of the mean?

A) 42 ÷
B) 42 ÷
C) 10 ÷ 42
D) 10 ÷

Question 22

The standard deviation of the sampling distribution of means is called the ______________.

A) sample deviation.
B) deviation of means
C) expected value
D) standard error of the mean

Question 23

In a sampling distribution of means, z-scores are in __________ units.

A) squared
B) metric
C) standard error
D) deviation score

Question 24

In order to use the z-score formula for determining the probability of obtaining a sample mean, we need all of the following, except _____________.

A) N
B) σₘ
C) μ
D) M

Question 25

The correct notation for determining the probability associated with sample means above 25 is _____________.

A) M = 25 + (z)(σₘ)
B) p(M > 25)
C) M = z + (25)(σₘ)
D) p(μ > 25)

Question 26

The formula used to convert a z-score to a sample mean includes all of the following elements, except __________.

A) μ
B) z
C) σ
D) σₘ

Question 27

Given a population mean of 78 and a standard error of the mean value of 2, what else do we need to use the formula to find the range of means that would be expected to occur 90% of the time?

A) The z-scores associated with the extreme high and low .1000 ends of the distribution.
B) The z-scores associated with the proportions between the mean and .1000.
C) The z-scores associated with extreme high and low .0500 ends of the distribution.
D) The z-scores associated with the proportion between the mean and .0500.

Question 28

M = μ + (z)(σ_M) is used to

A) locate the z-score associated with a certain mean.
B) convert a z-score to a sample mean.
C) convert a sample mean to a z-score.
D) find the probability associated with a certain mean.

Question 29

In order to determine the proportion of sample means expected to lie above 95% of the distribution, look in column ______ of the normal distribution table.

A) A
B) B
C) C
D) D

Question 30

Standard error

A) should be avoided.
B) is a standard deviation.
C) is due to mistakes made while collecting data.
D) has to be deducted from the standard deviation.

Question 31

Given a normally shaped distribution with a μ = 100 and a σ = 16, a sample of 36 individuals is randomly selected. The mean of the sample was 107. The z-score for the sample mean would be _______.

A) +2.62
B) -2.62
C) +.44
D) -.44

Question 32

A normally shaped distribution has a μ = 36 and a σ = 12. A sample of 9 individuals is randomly selected and achieved a M = 32. What is the z-score for the obtained sample mean?

A) -.33
B) +.33
C) -1.00
D) +1.00

Question 33

The scores from a population resulted in a normally shaped distribution with a μ = 52 and a σ_M = 3. The obtained sample mean of 47 converted to a z-score of _________.

A) +.56
B) -.56
C) +1.67
D) -1.67

Question 34

A sample of n = 49 is drawn at random from a population with a μ = 78 and a σ = 14. What is the probability that the sample mean will be 82 or higher?

A) .3859
B) .9772
C) .0228
D) .6141

Question 35

A sample of n = 9 is drawn at random from a population with a μ = 32 and a σ = 9. The probability that the sample mean will be 34 or below is _________.

A) .1429
B) .5871
C) .2514
D) .7486

Question 36

A normally shaped distribution has a μ = 36 and a σ_M = 2. The probability that a randomly drawn sample of n = 25 will have a mean of 38 or above is _________.

A) .0228
B) .9772
C) .1587
D) .8413

Question 37

A population of scores is normally distributed with a μ = 95 and a σ_M = 5. The probability that a randomly drawn sample of n = 12 will have a mean of 88 or above is _________.

A) .0808
B) .9192
C) .7190
D) .2810

Question 38

Given a normally shaped distribution with a μ = 62 and a σ_M = 5, what is p(M > 52)?

A) .9772
B) .0228
C) .0047
D) .9953

Question 39

If a distribution is normally shaped with a μ = 40 and a σ_M = 4, what is p(M < 38)?

A) .6915
B) .3085
C) .8413
D) .1587

Question 40

A random sample of n = 25 individuals is drawn from a population with a μ = 63 and a σ = 9. The probability is .1000 that the mean of the sample will be above what value?

A) -1.28
B) +1.28
C) 65.3
D) 60.70

Question 41

A sample of n = 36 individuals is drawn at random from a population that has a μ = 105 and a σ = 18. The probability is .0500 that the mean of the sample will be below what value?

A) 75.3
B) 134.7
C) 109.95
D) 100.05

Question 42

Explain what is meant by expected value.

Question 43

A standardized assessment inventory on the personality characteristic of "Perfectionism" has a μ = 70 and a σ = 12.
a. Compute σM for a sample of n = 100.
b. Compute σM for a sample of n = 25.
c. How is σM affected by sample size?

Question 44

Given a normally shaped population distribution with a μ = 24 and a σ = 5, what is the probability that an obtained sample of size n = 8 will have a mean that is
a. above 21?
b. above 27?
c. below 27?

Question 45

A psychologist has developed an assessment instrument to measure the degree of people's desire for privacy. The test has been standardized with a μ = 60 and a σ = 12. If a sample of size n = 24 is drawn at random, determine
a. p(M < 55).
b. P(M > 58).
c. p(M < 58).

Question 46

A population distribution is normally distributed with a μ = 57 and a σ = 7. What is the probability of obtaining a sample mean less than 55 if n = 18?

Question 47

A random sample of size n = 48 is drawn from a normally shaped distribution with a μ = 110 and a σ = 17. What is the probability that the mean of the sample will be greater than 104?

Question 48

A population distribution is normally distributed with a μ = 93 and a σ = 13. If n = 50, what proportion of sample means can be expected to be less than 97?

Question 49

A random sample of size n = 40 is randomly drawn from a population that is normally distributed with a μ = 82 and a σ = 13. The probability is .02 that the sample mean will be above what value?

Question 50

A normally shaped population distribution has μ = 55 and a σ = 5. If samples of size n = 20 are drawn at random, what range of sample means would be expected to occur 98% of the time?