Deck 8: Samples, Sampling Distributions, and Confidence Intervals

Question 1

Sampling distributions show the procedures for getting a random sample.

Answer 1

False

Question 2

To use a sample is to agree to accept some uncertainty about the results.

Answer 2

True

Question 3

Typically, samples used in research are random samples.

Answer 3

False

Question 4

The Central Limit Theorem describes the form of a sampling distribution.

Question 5

Your text recommended adding shading to a graph to indicate the width of a confidence interval.

Question 6

A confidence interval gives numbers calculated to bracket the population mean.

Question 7

A population with a rectangular distribution could produce a normally distributed sampling distribution.

Question 8

To know degrees of freedom, you must know the sample mean.

Question 9

To look up a t value in the t distribution table, you must know sample size.

Question 10

Sampling distributions are based on random samples.

Question 11

By using random samples, uncertainty about the conclusion can be eliminated.

Question 12

Researchers routinely use random samples for their research.

Question 13

The Central Limit Theorem describes the limits of a confidence interval.

Question 14

Your text recommended adding asterisks to a graph to indicate the width of a confidence interval.

Question 15

A confidence interval is a statistic with two numbers.

Question 16

A population with a bimodal distribution could produce a normally distributed sampling distribution.

Question 17

To know degrees of freedom, you must know the standard error of the mean.

Question 18

Sampling distributions are the basis of probability statements in statistics.

Question 19

To select a random sample, every member of the population must be identified.

Question 20

Studies that use nonrandom samples are rare among researchers.

Question 21

The Central Limit Theorem describes how to draw a random sample.

Question 22

To convey confidence intervals on a graph, your text recommended adding circles to a graph with the diameter proportional to the width of the confidence interval.

Question 23

Meaningful confidence intervals of 90, 95 and 99 percent could be calculated for a single sample mean.

Question 24

Using the techniques in Chapter 8, you can determine probabilities about sample means.

Question 25

To know degrees of freedom, you must know the sample size.

Question 26

The Central Limit Theorem applies only to the mean.

Question 27

Data Set 8-1: A sample with scores: 1, 2, 3

-Refer to Data Set 8-1. What is the probability of obtaining such a sample mean or one larger from a population in which µ = 0 and $\sigma$ = 1?

A) .4772
B) .0228
C) .4997
D) .0003
E) .4986
F) .0014
G) .4927
H) .0073

Question 28

Data Set 8-1: A sample with scores: 1, 2, 3

-Refer to Data Set 8-1. What is the probability of obtaining such a sample mean or one smaller from a population in which µ = 3 and $\sigma$ = 1?

A) .0418
B) .1587
C) .3414
D) .4582

Question 29

Data Set 8-1: A sample with scores: 1, 2, 3

-Refer only to Data Set 8-1. The 95 percent confidence interval about this sample mean is

A) 1.20 to 2.80
B) -.43 to 3.43
C) -2.30 to 6.30
D)-0.48 to 4.48

Question 30

Data Set 8-1: A sample with scores: 1, 2, 3

-Refer only to Data Set 8-1. The 99 percent confidence interval about this sample mean is

A) -7.93 to 11.93
B) -5.31 to 5.31
C) -3.73 to 7.73
D) -1.31 to 5.31
E) -1.37 to 5.37

Question 31

Data Set 8-2: A sample with scores: 2, 4, 6

-Refer to Data Set 8-2. What is the probability of obtaining such a sample mean or one smaller from a population in which $\mu$ = 5 and $\sigma$ = 2?

A) .0668
B) .1922
C) .3078
D) .3085

Question 32

Data Set 8-2: A sample with scores: 2, 4, 6

-Refer to Data Set 8-2. What is the probability of obtaining such a sample mean or one larger from a population in which $\mu$ = 3 and $\sigma$ = 3?

A) .1587
B) .2190
C) .2810
D) .3707

Question 33

Data Set 8-2: A sample with scores: 2, 4, 6

-Refer only to Data Set 8-2. The 95 percent confidence interval about this sample mean is

A) 1.13 to 6.87
B) 0.33 to 7.67
C) -4.61 to 12.61
D) -.97 to 8.97

Question 34

Data Set 8-2: A sample with scores: 2, 4, 6

-Refer only to Data Set 8-2. The 99 percent confidence interval about this sample mean is

A) -25.78 to 33.78
B) -7.46 to 15.46
C) -2.74 to 10.74
D) -2.62 to 10.62

Question 35

Data Set 8-3 :From a random sample of 36 college students the following statistics were obtained on the Milligram "Could You Be a Nazi?" shock test. The higher the score on this test the more the person obeys authority: = 300 volts, = 60 volts.

-The 95 percent confidence interval about the mean in Data Set 8-3 is

A) 177.48 to 422.52
B) 279.58 to 320.42
C) 296.60 to 303.40

Question 36

Data Set 8-3 :From a random sample of 36 college students the following statistics were obtained on the Milligram "Could You Be a Nazi?" shock test. The higher the score on this test the more the person obeys authority: = 300 volts, = 60 volts.

-The 99 percent confidence interval about the mean in Data Set 8-3 is

A) 135 to 465
B) 272.50 to 327.50
C) 295.42 to 304.58

Question 37

Data Set 8-3 :From a random sample of 36 college students the following statistics were obtained on the Milligram "Could You Be a Nazi?" shock test. The higher the score on this test the more the person obeys authority: = 300 volts, = 60 volts.

-Look at Data Set 8-3. In Milgram's original study using a cross-section of Americans, the population mean was 285 volts and the population standard deviation was 60. What is the probability of obtaining a mean like that of the college students (or a higher mean) from the population of Americans?

A) 1.50
B) .4332
C) .0668
D) .0987
E) .4013

Question 38

Data Set 8-4 :A random sample of 64 students produced the following statistics: = 18.00, = 7.00.

-For Data Set 8-4 the probability of obtaining such a sample mean (or one smaller) from a population with a mean of 20 and a standard deviation of 8 is

A) .4772
B) .4013
C) .0987
D) 0.0228

Question 39

Data Set 8-4 :A random sample of 64 students produced the following statistics: = 18.00, = 7.00.

-The 95 percent confidence interval about the mean in Data Set 8-4 is

A) 16.25 to 19.75
B) 17.78 to 18.22
C) 4 to 32

Question 40

Data Set 8-4 :A random sample of 64 students produced the following statistics: = 18.00, = 7.00.

-The 99 percent confidence interval about the mean in Data Set 8-4 is

A) -0.69 to 36.69
B) 17.71 to 18.29
C) 15.67 to 20.33

Question 41

Data Set 8-5Suppose you drew a random sample of 100 from a population and found $\bar { X }$ = 30.

-Look at Data Set 8-5. What is the probability that this sample (or one with a larger mean) was drawn from a population in which µ = 29.75 and $\sigma$ = 1?

A) .0062
B) .4013
C) .4938

Question 42

Data Set 8-5Suppose you drew a random sample of 100 from a population and found $\bar { X }$ = 30.

-Look at Data Set 8-5. What is the probability that this sample (or one with a larger mean) was drawn from a population in which, $\mu$ = 29.75 if $\sigma$ = 4?

A) .0239
B) .4761
C) .2357
D) .2643

Question 43

Data Set 8-6 :A population mean (µ) of 5 and a standard deviation ( $\sigma$ ) of 2.

-See Data Set 8-6. If N = 3, what proportion of the means of a sampling distribution would be less than 4.0?

A) .0668
B) .1922
C) .3078
D) .3085

Question 44

Data Set 8-6 :A population mean (µ) of 5 and a standard deviation ( $\sigma$ ) of 2.

-See Data Set 8-6. If N = 5, what proportion of the means of a sampling distribution would be greater than 6.0?

A) .4938
B) .3686
C) .3085
D) .1314
E) .0062

Question 45

Data Set 8-7: A population with a mean (µ) of 10 and a standard deviation ( $\sigma$ ) of 1. (Carry 3 or 4 decimals in your calculations.)

-See Data Set 8-7. If N = 3, what proportion of the means of a sampling distribution would be larger than 12?

A) .4772
B) .0228
C) .4997
D) .0003
E) .4986
F) .0014
G) .4927
H) .0073

Question 46

Data Set 8-7: A population with a mean (µ) of 10 and a standard deviation ( $\sigma$ ) of 1. (Carry 3 or 4 decimals in your calculations.)

-What is the probability that a random sample with N = 7 from Data Set 8-7 would have a mean of 9 or smaller?

A) .0557
B) .1587
C) .3414
D) .4443
E) .4960
F) 0.0040

Question 47

Data Set 8-8: A population with a mean (µ) of 5 and a standard deviation ( $\sigma$ ) of 3. (Carry 3 or 4 decimals in your calculations.)

-See Data Set 8-8. If N = 3, what proportion of the means of a sampling distribution would be larger than 6?

A) .1587
B) .2190
C) .2810
D) .3707

Question 48

Data Set 8-8: A population with a mean (µ) of 5 and a standard deviation ( $\sigma$ ) of 3. (Carry 3 or 4 decimals in your calculations.)

-See Data Set 8-8. If N = 6, what proportion of the means of a sampling distribution would be smaller than 4?

A) .0228
B) .1293
C) .2061
D) .2939
E) .3707
F) .4772

Question 49

Data Set 8-9: A population mean (µ) of 4 and a standard deviation ( $\sigma$ ) of 2. (Carry 3 or 4 decimal places in your calculations.)

-See Data Set 8-9. If N = 5, what proportion of the means of sampling distribution would be larger than 6?

A) .4875
B) .3413
C) .1587
D) .0125

Question 50

Data Set 8-9: A population mean (µ) of 4 and a standard deviation ( $\sigma$ ) of 2. (Carry 3 or 4 decimal places in your calculations.)

-What is the probability that a random sample with N = 7 from Data Set 8-9 would have a mean of 3 or less?

A) .4998
B) .4066
C) .3085
D) 19.15
E) .0934
F) .0002

Question 51

Data Set 8-10: A population with a mean (µ) of 6 and a standard deviation ( $\sigma$ ) of 2. (Carry 3 or 4 decimals in your calculations.)

-See Data Set 8-10. If N = 4, what proportion of the means of a sampling distribution would be less than 3? (Drawing the sampling distribution may help.)

A) .0013
B) .0668
C) .2401
D) .4332
E) .4987

Question 52

Data Set 8-10: A population with a mean (µ) of 6 and a standard deviation ( $\sigma$ ) of 2. (Carry 3 or 4 decimals in your calculations.)

-What is the probability that a random sample with N = 8 from Data Set 8-10 would have a mean of 7 or larger?

A) .00003
B) .1915
C) .3085
D) .4207
E) .49997
F) 0.0793

Question 53

Summary statistics from a sample were: $\Sigma$ X² = 36, $\Sigma$ X = 12, and N = 6. The standard error of the mean is

A) 0.26
B) 0.40
C) 0.58
D) 0.63
E) 0.98

Question 54

Summary statistics from a sample were: $\Sigma$ X² = 50, $\Sigma$ X = 15, and N = 6. The standard error of the mean is

A) 0.264
B) 0.417
C) 0.589
D) 1.021
E) 0.65

Question 55

Summary statistics from a sample were: $\Sigma$ X² = 66, $\Sigma$ X = 12, and N = 4. The standard error of the mean is

A) 0.79
B) 1.37
C) 1.58
D) 2.50
E) 5.00

Question 56

Summary statistics from a sample were: $\Sigma$ X = 18, $\Sigma$ X² = 118, and a sample size of 3. The standard error of the mean is

A) 1.581
B) 1.496
C) 1.054
D) 0.745
E) 1.29

Question 57

Summary statistics from a sample were: $\Sigma$ X² = 60, $\Sigma$ X = 10, and a sample size of 5. The standard error of the mean is

A) 0.40
B) 0.57
C) 0.80
D) 0.89
E) 1.79
F) 1.41

Question 58

Summary statistics from a sample were: $\Sigma$ X = 8, $\Sigma$ X² = 46, and a sample size of 4. The standard error of the mean is

A) 0.791
B) 1.369
C) 1.581
D) 1.826

Question 59

Summary statistics from a sample were: $\Sigma$ X² = 6, $\Sigma$ X= 3, N = 2. The standard error of the mean is

A) 0.37
B) 0.61
C) 0.87
D) 1.23

Question 60

Summary statistics from a sample were: $\Sigma$ X² = 60, $\Sigma$ X = 20, N = 10. The standard error of the mean is

A) 0.15
B) 0.22
C) 0.45
D) 0.47
E) 0.70

Question 61

Summary statistics from a sample were: $\Sigma$ X² = 36, $\Sigma$ X= 10, N = 5. The standard error of the mean is

A) 0.40
B) 0.57
C) 0.80
D) 0.89
E) 1.79

Question 62

In the story at the beginning of the chapter, the question the students were trying to answer was

A) Does random sampling work?
B) How much error does a random sample produce?
C) What is the family income of a sample of State U students?
D) What is the family income of State U students?

Question 63

In the story at the beginning of the chapter, the students' principal interest was in the family income of

A) the biased sample of State U students
B) the random sample of State U students
C) State U students
D) all students.

Question 64

In the story at the beginning of the chapter, the interest of the students was in

A) whether or not random samples produce accurate results
B) how much money is spent at their campus center by a typical student
C) why their university's tuition had increased so dramatically in 5 years
D) the mean income of families of students at their university.

Question 65

With respect to populations, your text says that they are

A) generally important
B) generally unmeasurable
C) characterized by parameters
D) all of the other alternatives are correct.

Question 66

One way to reduce uncertainty to zero is to

A) draw a large sample (over 100)
B) measure the population
C) either of the descriptive alternative are correct
D) neither of the descriptive alternatives is correct.

Question 67

Uncertainty about a population can be eliminated if you

A) use a large random sample
B) obtain data from all members of the population
C) both of the descriptive alternatives
D) neither of the descriptive alternatives.

Question 68

Uncertainty regarding conclusions about a population can be eliminated by

A) drawing a sample
B) drawing a large sample
C) drawing a large random sample
D) none of the other alternatives are correct.

Question 69

Which of the following is (are) not true? To draw a sample

A) is to accept some uncertainty about the conclusions
B) enables you to calculate parameters
C) is to risk drawing the wrong conclusions about the population
D) all of the other alternatives are correct.

Question 70

When the participants who arrive for a study are assigned to a group on the basis of chance,

A) random assignment occurred
B) random sampling occurred
C) the statistical conclusions will be exact
D) all of the other alternatives are correct.

Question 71

Random assignment means

A) every sample of a particular size in a population has an equal chance of being included in the study
B) the participants in a study are assigned to a group on the basis of chance
C) statistics will be exactly equal to parameters
D) none of the other alternatives are correct.

Question 72

According to the procedure that your text described for obtaining a random sample, one member of the population can be in the sample__________ times.

A) one
B) two
C) three
D) as many times as that member turns up in the random sampling procedure.

Question 73

According to your text, if you draw a random sample, you are assured that

A) the sample will mirror the population
B) you will be always uncertain about the population
C) the conclusions you draw will be correct
D) none of the other alternatives are correct

Question 74

A random sample is one

A) that is haphazard
B) that is unplanned
C) in which every sample of a particular size has an equal probability of being selected
D) any of the other alternatives are correct.

Question 75

Random assignment is a procedure that

A) gives every sample from a population an equal chance of being selected
B) ensures that there will be no uncertainty in the conclusions
C) assigns the available participants to groups
D) all of the other alternatives are correct.

Question 76

A random sample is always

A) large
B) representative
C) one of many possible samples
D) all of the other alternatives are correct.

Question 77

A random sample

A) is more likely to be representative than any other kind
B) is representative
C) allows you to calculate the parameters of the population
D) none of the other alternatives are correct.

Question 78

Having a random sample means

A) every sample of a particular size in the population has an equal chance of being included in the study
B) the participants in a study are assigned to groups by alternations
C) statistics will be exactly equal to parameters
D) none of the other alternatives are correct.

Question 79

Which of the following fits your text's definition of a random sample of a city?

A) every fourth name in the telephone book
B) every 10th name on the list of property owners
C) 50 names picked by the mayor as a representative sample
D) none of the other alternatives are correct.

Question 80

Which of the following is a random sample of a college student body?

A) every fifth person coming out of the Campus Center between 8:30 and 10:00 a.m.
B) Laura Hankins, whose registration number corresponded to the number picked from a table of random numbers
C) every 20th person in the student directory
D) none of the other alternatives are correct.