Chapter 6: Probability, Probability Distributions, and an Introduction to Inferential Statistics

Test Bank

Multiple Choice

1. Probability would fall into the class of ______.

a. descriptive statistics

b. inferential statistics

c. causal statistics

d. generalizability statistics

Learning Objective: 6.1. Explain the basic notion of probability of being in “the long run” compared with predictions of single cases.

Cognitive Domain: Knowledge

Answer Location: Introduction

Difficulty Level: Easy

2. Probability can be defined as ______.

a. the number of times a specific even can occur relative to the total number of times that any event can occur

b. the total number of possible outcomes minus the number of ways a particular outcome may occur

c. the total number of ways a possible outcome can occur

d. the likelihood that the researcher would reject the null hypothesis

Learning Objective: 6.1. Explain the basic notion of probability of being in “the long run” compared with predictions of single cases.

Cognitive Domain: Knowledge

Answer Location: Probability. What is it good for? Absolutely everything!

Difficulty Level: Easy

3. The bounding rule of probabilities state that ______.

a. probabilities can be less than zero

b. probabilities can be greater than one

c. probabilities can be both less than zero and greater than one

d. probabilities can never be less than zero and greater than one

Learning Objective: 6.5. Identify the rules of probability.

Cognitive Domain: Knowledge

Answer Location: Probability. What is it good for? Absolutely everything!

Difficulty Level: Easy

4. The complement of an event is ______.

a. the set of all outcomes that are not the event of interest

b. the set of all outcomes that are and are not the event of interest

c. an event that is very similar to the event of interest

d. works alongside the event of interest

Learning Objective: 6.5. Identify the rules of probability.

Cognitive Domain: Knowledge

Answer Location: The rules of probability.

Difficulty Level: Easy

5. When the joint probability of two events occurring is zero, the two events are said to be ______.

a. mutually exclusive

b. complementary

c. restrictive

d. additive

Learning Objective: 6.2. Describe the notion of independence between variables.

Cognitive Domain: Knowledge

Answer Location: The rules of probability.

Difficulty Level: Easy

6. The restricted addition rule of probabilities relates to ______.

a. determining the number of different ways a particular outcome can occur

b. the probability of either of two mutually exclusive events occurring is equal to the sum of their separate probabilities

c. the fact that the probability of an event occurring is between 0 and 100

d. the probability of two non-mutually exclusive events occurring is equal to the sum of their separate probabilities

Learning Objective: 6.2. Describe the notion of independence between variables.

Cognitive Domain: Knowledge

Answer Location: The rules of probability.

Difficulty Level: Easy

7. The following equation, , represents ______.

a. conditional probability

b. restrictive multiplication rule of probabilities

c. restrictive addition rule of probabilities

d. general addition rule of probabilities

Learning Objective: 6.2. Describe the notion of independence between variables.

Cognitive Domain: Comprehension

Answer Location: The rules of probability.

Difficulty Level: Medium

8. Which rule of probability states that for two non-mutually exclusive events the probability of each event occurring is equal to the sum of their separate probabilities minus the probability of their joint occurrences?

a. bounding rule of probabilities

b. restricted addition rule of probabilities

c. general addition rule of probabilities

d. restricted multiplication rule of probabilities

Learning Objective: 6.2. Describe the notion of independence between variables.

Cognitive Domain: Knowledge

Answer Location: The rules of probability.

Difficulty Level: Easy

9. The following equation, , represents ______.

a. conditional probability

b. restrictive multiplication rule of probabilities

c. restrictive addition rule of probabilities

d. general addition rule of probabilities

Learning Objective: 6.2. Describe the notion of independence between variables.

Cognitive Domain: Comprehension

Answer Location: The rules of probability.

Difficulty Level: Medium

10. The question “What is the probability of a child being in school or the child offending?” is an example of ______.

a. general multiplication rule of probabilities

b. restrictive multiplication rule of probabilities

c. restrictive addition rule of probabilities

d. general addition rule of probabilities

Learning Objective: 6.2. Describe the notion of independence between variables.

Cognitive Domain: Knowledge

Answer Location: The rules of probability.

Difficulty Level: Easy

11. Which rule of probability states that for two mutually exclusive events the probability of each event occurring is equal to the product of their separate probabilities?

a. bounding rule of probabilities

b. restricted addition rule of probabilities

c. general addition rule of probabilities

d. restricted multiplication rule of probabilities

Learning Objective: 6.2. Describe the notion of independence between variables.

Cognitive Domain: Knowledge

Answer Location: The rules of probability.

Difficulty Level: Easy

12. The following equation, , represents ______.

a. general multiplication rule of probabilities

b. restrictive multiplication rule of probabilities

c. restrictive addition rule of probabilities

d. general addition rule of probabilities

Learning Objective: 6.3. Describe the difference between conditional and unconditional probabilities.

Cognitive Domain: Comprehension

Answer Location: The rules of probability.

Difficulty Level: Medium

13. A binominal distribution has a variable that ______.

a. consists of three categories

b. consists of only one category

c. consists of multiple categories

d. consists of two categories

Learning Objective: 6.6. Describe how probability distributions are used to test hypotheses.

Cognitive Domain: Knowledge

Answer Location: A discrete probability distribution—The binomial distribution

Difficulty Level: Easy

14). The following equation. , can be used to determine the probability of any number of successes, r, so long as there are only two outcomes—success(p) and failure(q). This is also called the ______.

a. probability theorem

b. binomial theorem

c. proportion theorem

d. probability distribution theorem

Learning Objective: 6.6. Describe how probability distributions are used to test hypotheses.

Cognitive Domain: Comprehension

Answer Location: A discrete probability distribution—The binomial distribution

Difficulty Level: Medium

15. When testing the null hypothesis a researcher begins with the assumption that ______.

a. the researcher can prove the null hypothesis is false

b. the researcher can prove the alternative hypothesis is false

c. the alternative hypothesis is true

d. the null hypothesis is true

Learning Objective: 6.7. State the difference between a null and a research hypothesis.

Cognitive Domain: Knowledge

Answer Location: Hypothesis testing with the binomial distribution

Difficulty Level: Easy

16. The risk we take in rejecting a true null hypothesis is called ______.

a. significance or alpha ()

b. assumption of null hypothesis

c. statistical power

d. type II error

Learning Objective: 6.7. State the difference between a null and a research hypothesis.

Cognitive Domain: Knowledge

Answer Location: Hypothesis testing with the binomial distribution

Difficulty Level: Easy

17. If an infinite number of random samples of size n are drawn from any population with mean µ and standard deviation σ, then as the sample size (n) becomes large, the sampling distribution of sample means will approach normality even if the population distribution is not normally distributed is known as the ______.

a. central limit theorem

b. normal distribution

c. sampling distribution

d. standard normal probability distribution

Learning Objective: 6.9. Describe why probability theory is important for criminological and criminal-justice-related research.

Cognitive Domain: Comprehension

Answer Location: Samples, populations, sampling distributions, and the central limit theorem

Difficulty Level: Medium

True/False

18. Events that have only two possible outcomes are called Bernoulli Events

Learning Objective: 6.5. Identify the rules of probability.

Cognitive Domain: Knowledge

Answer Location: A discrete probability distribution—The binomial distribution

Difficulty Level: Easy

19. For every normal distribution, .3413 (34.13%) of the are under the curve lies between the mean and a point that is one standard deviation either to the right or the left of the mean.

Learning Objective: 6.8. Identify areas under the normal curve and how we can transform values from a variable distribution to z scores and determine the probability of their occurrence.

Cognitive Domain: Comprehension

Answer Location: The area under the normal curve

Difficulty Level: Medium

20. For every normal distribution, .6826 (68.26%) of the are under the curve lies between the mean and a point that is one standard deviation to the right and one standard deviation to the left of the mean.

Learning Objective: 6.8. Identify areas under the normal curve and how we can transform values from a variable distribution to z scores and determine the probability of their occurrence.

Cognitive Domain: Comprehension

Answer Location: The area under the normal curve

Difficulty Level: Medium

21. For every normal distribution, .9544 (95.44%) of the are under the curve lies between the mean and a point that is two standard deviations to the right and two standard deviations to the left of the mean

Learning Objective: 6.8. Identify areas under the normal curve and how we can transform values from a variable distribution to z scores and determine the probability of their occurrence.

Cognitive Domain: Comprehension

Answer Location: The area under the normal curve

Difficulty Level: Medium

22. In a normal distribution, a z-score of at least 1.96 is indicative of a rare event because it occurs 5% of the time or less

Learning Objective: 6.8. Identify areas under the normal curve and how we can transform values from a variable distribution to z scores and determine the probability of their occurrence.

Cognitive Domain: Comprehension

Answer Location: The area under the normal curve

Difficulty Level: Medium

23. The larger a sample is the more imprecise the estimates are.

Learning Objective: 6.8. Identify areas under the normal curve and how we can transform values from a variable distribution to z scores and determine the probability of their occurrence.

Cognitive Domain: Comprehension

Answer Location: The area under the normal curve

Difficulty Level: Easy

24. For every normal distribution, .9974 (99.74%) of the are under the curve lies between the mean and a point that is three standard deviations to the right and is three standard deviations to the left of the mean

Learning Objective: 6.8. Identify areas under the normal curve and how we can transform values from a variable distribution to z scores and determine the probability of their occurrence.

Cognitive Domain: Comprehension

Answer Location: The area under the normal curve

Difficulty Level: Medium

Essay

25. State and describe the three characteristics of the sampling distribution of the mean based on the Central Limit Theorem

Learning Objective: 6.9. Describe why probability theory is important for criminological and criminal-justice-related research.

Cognitive Domain: Knowledge/Application

Answer Location: Samples, populations, sampling distributions, and the central limit theorem

Difficulty Level: Hard