Deck 4: Some Key Ingredients for Inferential Statistics: the Normal Curve, Sample Versus Population, and Probability

Question 1

A person received a test score that was in the top 20% of everyone who has taken the test. The test scores are normally distributed. This person's Z score must be at least:

A).46
B).84
C)5.03
D)7.93

Answer 1

.84

Question 2

John attained a score of 65 on his stats exam. The mean for the class was a 70 with a SD of 10. What percentage of students scored below and above John?

A)31 and 69
B)40 and 60
C)45 and 55
D)10 and 90

Answer 2

31 and 69

Question 3

The mean score on a creativity test is 20 and the standard deviation is 5. The distribution is normal. Using the percentage approximations for the normal curve, how many people would attain a score between 15 and 25?

A)34%
B)14% + 34% = 48%
C)50%
D)34% + 34% = 68%

Answer 3

34% + 34% = 68%

Question 4

What IQ score would a person need to be in the top 5% of the general population? Assume M = 100 and SD = 16.

A)110.45
B)115.44
C)120.05
D)126.24

Question 5

The _____________ explains why many distributions tend to be close to normal in the real world.

A)central limit theorem
B)normal curve table
C)Pythagorean theorem
D)triples list calculation

Question 6

On a normal curve, what percentage of scores fall between a Z score of 1.29 and a Z score of 1.49?

A).54
B)3.04
C)1.85
D)6.05

Question 7

A person received a score of 4.78 on a test. This turned out to be a Z score of +1.5. What percentage are above this score? Assume a normal distribution.

A)43.32% - 50% = -6.68%
B)50% - 43.32% = 6.68%
C)100% - 43.32% = 56.68%
D)50% + 43.32% = 83.32%

Question 8

What Z score would a person need to be in the 4% of his or her class on a particular test? Assume a normal distribution.

A)4% - 50% = -46%, which corresponds to a Z score of -1.75
B)50% - 46% = 4%, which corresponds to a Z score of .10
C)50% - 4% = 46%, which corresponds to a Z score of 1.75
D)34% + 14% - 4% = 44%, which corresponds to a Z score of 1.55 or 1.56

Question 9

A person received a test score that is in the top 32% and the test scores follow a normal curve. This person's Z score must be at least:

A).46
B)1.5
C)2.8
D).91

Question 10

If you were looking at a graph of a normal distribution, which of the following would best describe it?

A)Bimodal and roughly symmetrical
B)Unimodal, roughly symmetrical, and bell-shaped
C)Skewed to the right
D)Roughly symmetrical and W-shaped

Question 11

Carrie attained a score of 650 on the verbal section of her SAT. The mean grade was a 500 with a standard deviation of 100. What percentage of test takers scored below and above Carrie?

A)85 and 15
B)10 and 90
C)93 and 7
D)more information is required to answer this question

Question 12

The normal curve table shows percentages of scores:

A)between a correlation of -1 and +1
B)between a correlation of 0 and -1
C)between the median and various numbers of Z scores above the median
D)between the mean and various numbers of Z scores above or below the mean

Question 13

Using the percentage approximations for the normal curve, what percentage of scores are between the mean and one standard deviation below the mean?

A)14%
B)50% - 34% = 16%
C)34%
D)50%

Question 14

A particular nation has a human rights score of 41, which equals a Z score of 1.3. What is the percentage of nations above this score? (Assume a normal distribution.)

A)40.32% - 50% = -9.68%
B)50% - 40.32% = 9.68%
C)100% - 40.32% = 59.68%
D)50% + 40.32% = 99.68%

Question 15

The mean score on a political attitude scale is 5 and the standard deviation is 2. The distribution is normal. Using the percentage approximations for the normal curve, how many people would get a score between 5 and 9?

A)34%
B)34% + 14% = 48%
C)50%
D)34% + 34% = 68%

Question 16

What Z score would a person need to be in the top 5%? Assume a normal distribution.

A)5% - 50% = -45%, which corresponds to a Z score of -1.64
B)-5%, which corresponds to a Z score of -.12
C)5%, which corresponds to a Z score of .12
D)50% - 5% = 45%, which corresponds to a Z score of 1.64

Question 17

If a person has an IQ of 130, approximately what percentage of people have higher IQs? Assume M = 100 and SD = 16.

A)1%
B)3%
C)6%
D)9%

Question 18

Distributions observed in nature and research commonly approximate:

A)a kurtotic curve
B)a multimodal, symmetric curve
C)a normal curve
D)a bimodal, asymmetric curve

Question 19

Jake's Z score for running ability is .60. What is Jake's raw score (assuming M =100 and SD = 7).

A)raw score = 100.1
B)raw score = 104.2
C)raw score = 93.5
D)raw score = 103.2

Question 20

A person has a score that is in the bottom 42% of the scores. What is the highest Z score this person could have? (Assume a normal distribution.)

A)-1.41
B)-)94
C)-)20
D)+)25

Question 21

You randomly select someone from a group of 12. Two of those in the group were born in Iowa. What is the chance you will pick a person born in Iowa?

A)1/12 = .08
B)2/12 = .17
C)12/2 = 6
D)12* 2 = 24

Question 22

The fact that probabilities are proportions means that they:

A)have to be larger than one
B)can't be lower than zero or more than one
C)can't be lower than zero or more than .05
D)can be either a positive or a negative number

Question 23

In a housing project there are 350 households in which English is usually spoken, 50 in which Spanish is usually spoken, and 100 in which the language is other than English or Spanish. A researcher approaches a house at random to conduct an interview. What is the chance that the usual language in that household will NOT be English?

A)1/500 = .002
B)50/350 = .14
C)150/500 = .3
D)150/350 = .43

Question 24

You wish to survey the interests of students in your statistics class. You enter the names of all students onto an Excel spreadsheet. You then use a computer program to generate a list of random names. This is called:

A)computerized selection
B)haphazard selection
C)sampling selection
D)random selection

Question 25

A researcher conducts extensive interviews with 40 workers at a large factory in order to examine the morale among workers in general at that factory. In this example, what is the population?

A)The 40 workers interviewed
B)All workers in the factory except the 40 interviewed
C)All the workers in the factory
D)All the factory workers in the United States.

Question 26

Survey organizations in the United States today are not allowed to call ____________ , creating some bias in the poll results.

A)individuals of African American descent
B)individuals over the age of 60
C)cell phones
D)registered voters

Question 27

You have an aquarium full of tropical salt-water fish and you need to know the exact salt content of the water. To test it, you take a cup and scoop some of the water out. In statistical language, the scoop of water is a:

A)population
B)parameter
C)sample
D)population distribution

Question 28

The Gallup Poll correctly predicted George H. W. Bush's 1988 victory using only 4,089 interviews. Why, then, did the Gallup Poll in 1948 wrongly predict Dewey's victory over Truman when they used 50,000 interviews to make the prediction?

A)They only interviewed people in one state
B)They used multistage cluster sampling
C)They used quota sampling
D)They used random sampling

Question 29

Relative frequency is:

A)the expected number of times you will obtain a particular outcome in an experiment
B)how frequently a result occurs
C)what result you expect if you repeat an experiment frequently
D)the number of times something occurs relative to the number of times it could have occurred

Question 30

In figuring probabilities, expected relative frequency is:

A)how many times something happens
B)the result of an experiment
C)the number of successful outcomes divided by the number of total outcomes expected if you repeat an experiment a large number of times
D)the number of unsuccessful outcomes multiplied by the number of successful outcomes expected if you repeat an experiment a large number of times

Question 31

You want to study the general amount of drug use at your university. You obtain a complete list of students. You then put all the names into a box and have a blindfolded person select as many people as you needed. This is called:

A)random selection
B)haphazard selection
C)specified selection
D)type B selection

Question 32

Since 1948, all survey organizations have used the "probability method" to increase the accuracy of their results. What type of sampling method is utilized as part of this new method?

A)Multistage cluster sampling
B)Unitary cluster sampling
C)Quota sampling
D)Inferential sampling

Question 33

To change a proportion into a percent:

A)divide by 10
B)multiply by 100
C)take the square root of the value
D)multiply by 10

Question 34

If you were to select a score at random from a distribution that follows a normal curve, what approximately is the probability of selecting a score between Z scores of 0 and +1?

A)10%
B)55%
C)34%
D)14%

Question 35

You want to study the physical effects of caffeine. To recruit participants for your experiment you post a sign-up sheet for anyone willing to participate. This is an example of:

A)random selection
B)haphazard selection
C)stratified selection
D)type B selection

Question 36

In statistics writing, it is common to use Greek letters for:

A)haphazard sampling
B)quota sampling
C)cross-sectional studies
D)population parameters

Question 37

If you want to know something about a population, your results would be MOST accurate if you could study the:

A)entire population
B)subgroup from the population
C)top 5% of people from the population
D)top 50% of people from the population

Question 38

Whenever possible, researchers report the proportion of individuals approached for a study who actually participated. This is called:

A)attrition rate
B)random selection rate
C)approach rate
D)response rate

Question 39

In a single throw of a die, what is the probability of attaining a number of 4 or lower?

A).57
B).67
C).50
D).77

Question 40

The actual values of the mean, variance, and standard deviation of a population are called:

A)sample statistics
B)population parameters
C)population Z scores
D)regressed standardized scores

Question 41

The __________ interpretation of probability is the understanding of probability as the proportion of a particular outcome you would obtain if you were to repeat the experiment many times.

Question 42

A(n)__________ shows the percentage of scores between the mean and any particular Z score.

Question 43

In __________ sampling, the researcher often begins with a complete list of all the members of the population.

Question 44

The mean, standard deviation, and variance of a population are called population __________.

Question 45

In the context of probability, a(n)__________ is the result of an experiment (or virtually any event, such as a coin coming up heads or it raining tomorrow).

Question 46

Inferential statistics is the branch of statistics that draws conclusions about ___________ based on information in ___________.

Question 47

In a normal distribution approximately 68% of the scores are between a Z score of -1 and a Z score of __________.

Question 48

"______= .5" expresses in symbols that the probability is fifty-fifty that a particular thing will happen. (Give a letter or symbol.)

Question 49

The scores of the entire group of participants to which a researcher intends the results of a study to apply is called a(n)__________.

Question 50

A probability is a proportion. (True or False)

Question 51

In a normal curve approximately __________ percent of the scores are between one and two standard deviations above the mean.

Question 52

Sixty years ago opinion polls often used the __________ method of sampling, which is now largely discredited.

Question 53

You conduct a survey by giving out a questionnaire to the people you meet (and who are willing to take your questionnaire)on a given evening. You are using __________ selection.

Question 54

A(n)__________ refers to the scores of the particular set of people studied that are intended to represent the scores in some larger population.

Question 55

A(n)__________ refers to the larger group to which a researcher makes inferences based on the particular group of participants studied.

Question 56

Probability is the __________ relative frequency of a particular outcome.

Question 57

Today, survey sampling uses complex methods in order to ensure a close approximation to true __________ sampling.

Question 58

The mean, standard deviation, and variance of a sample are called sample ___________.

Question 59

In a normal curve approximately _________ percent of the scores are lower than two standard deviations below the mean.

Question 60

__________ selection is a procedure of selecting a sample of individuals to study such that each individual in the population has an equal chance of being selected.

Question 61

On a measure of writing ability, college students in general have a mean of 60, a standard deviation of 8, and the scores follow a normal distribution.
a. Approximately what percentage of college students have writing ability scores above 68? Above 76? Below 52? Between 52 and 60? Use the normal curve approximation rules.
b. Explain your answers and procedure to a person who is not familiar with the normal curve or normal curve areas.

Question 62

A researcher wishes to conduct a survey of caregivers of Alzheimer's disease patients in the United States regarding their attitudes toward their role and the difficulties they face. What would be the best way to select the caregivers to study? Explain what a researcher would do to a person who is unfamiliar with research methods or statistics. Why might it be difficult to gather a truly random sample in this case?

Question 63

You want to conduct a survey of students in a large dormitory. The survey will involve intensive interviews with each person who participates, so it will not be practical to interview everyone. What would be the best way to select particular individuals to interview? (Assume that whoever you ask to participate will be willing to do so.)Explain what you would do and why to a person who is unfamiliar with research methods or statistics.

Question 64

In almost any published research article, the Results section will describe the methods associated with determining statistical significance, followed by something like: "p < .05 or p < .01." (True or False)

Question 65

A business uses a 7-point scale about satisfaction with the services it provides to clients. The ratings are normally distributed with a mean of 4.8 and a standard deviation of .5.
What percentage of clients rate their satisfaction above a 5? Above a 6? Above 4? Below 4? Use the normal curve table and include a sketch.

Question 66

The number of words in the active vocabulary of children of a particular age is normally distributed with a mean of 3,000 and a standard deviation of 500.
a. How many words would a child of this age have to know to be in the top 2%? The top 16%? The top 50%? The bottom 2%? Use the normal curve approximation rules and include a sketch.
b. Explain your answers and procedure to a person who is not familiar with the normal curve or normal curve areas.

Question 67

On a test of optimism, scores of people diagnosed with a particular disease are normally distributed with a mean of 20 and a standard deviation of 5.
How high of a score does such a person with this disease need to be among the 5% most optimistic?
Among the 20% most optimistic? How low of a score to be among the 10% least optimistic?
Use the normal curve table and be sure to include a sketch.

Question 68

Provide an example of a variable that is normally distributed in the general population. Why is the normal curve so common in nature?

Question 69

On a test of physical fitness, 18-year-olds' scores are normally distributed with a mean of 140 and a standard deviation of 25.
a. Approximately what percentage of 18-year-olds have scores above 190? Below 165? Below 115?
Use the normal curve approximation rules and be sure to include a sketch.
b. Explain your answers and procedure to a person who is not familiar with the normal curve or normal curve areas.

Question 70

Modern public opinion polls are completely unbiased (100% accurate)at present. (True or False)

Question 71

The length of conversations between supervisors and workers in a particular manufacturing industry is normally distributed with a mean of 4.0 minutes and a standard deviation of .8 minutes.
What percentage of conversations are longer than 4.4 minutes? Longer than 5 minutes? Longer than 3 minutes? Shorter than 2.5 minutes? Use the normal curve table.