Test Bank

Chapter 6: Probability

Multiple Choice

1. What do inferential statistics allow researchers to do?

A. make definitive causal statements about the relationships between variables

B. plot correlational and causal relationships across variables

C. allow a researcher to use probability theory and make inferences about the population from which the sample was taken

D. use descriptive statistics in the formation of generalizations about the population from which the sample was drawn

2. The logical premises that form a set of predictions about the likelihood of certain events or the empirical results that one would expect to see in an infinite set of trials is the definition of which of the following?

A. probability theory

B. ecological fallacy

C. correlational theory

D. regression theory

3. A probability is defined as ______.

A. the likelihood that a certain even will occur

B. the correlational relationship existing between two categorical variables

C. the causal relationship existing between two categorical variables

D. the empirical likelihood of the mean acting as a statistically significant predictor

4. Mathematically, “p(A)” indicates which of the following?

A. the probability that Event A will occur

B. the probability that Event A will not occur

C. the probability that Event A is correlated with Event B

D. the correlational magnitude of Event A

5. Probabilities always sum to what?

A. 0

B. 0.50

C. There is no rule about the summation of probabilities.

D. 1.00

6. The major difference between proportions and probabilities is ______.

A. there is no difference, it is simply a different word used to describe the same thing

B. proportions represent predictions while probabilities are descriptive

C. proportions are descriptive while probabilities represent predictions

D. proportions are typically used in quantitative research while probabilities are used in qualitative research

7. In scientific inquiry, a prediction, grounded in logic, about whether or not a certain event will occur is also known as what?

A. a correlation

B. regression

C. theoretical prediction

D. probability theory

8. An empirical outcome is defined as ______.

A. a numerical result from a sample, such as a mean or frequency

B. a qualitative outcome from a categorical variable

C. a quantitative theoretical proposition regarding the nature of the association between two closely related categorical variables

D. a qualitative theoretical proposition regarding the nature of the association between two closely related categorical variables

9. An observed outcome is also known as what in scientific research?

A. theoretical prediction

B. probability distribution

C. probabilistic theory

D. empirical outcome

10. In the binomial distribution, the total number of ways that r successes can occur in a sample of size N is called what?

A. a descriptive

B. a distribution

C. a combination

D. a probability distribution

11. In statistics, 0! equals ______.

A. 0

B. 1

C. .1

D. There is no such term in the field of statistics.

12. In binomial probability theory, what does the symbol q represent?

A. the probability of a success

B. the probability of a failure

C. the probability of a statistically significant empirical outcome

D. the probability of no statistically significant empirical outcome

13. The guarantee that the probability of r successes and N − r failures is the product of p and q is known as which of the following in the field of statistics?

A. restricted multiplication rule for independent events

B. binomial probability mandate

C. binomial probability theory

D. binomial probability distribution

14. One nuance of the binomial probability distribution is that the p(r) column sums to ______.

A. 0

B. 1

C. −1

D. the absolute value of the binary coefficient

15. What is the technique used by scientists to standardize the normal curve?

A. converting the probabilities into basic percentages so the curve can be streamlined, facilitating further analyses

B. applying the standardized probability means to each curve

C. converting a distribution’s raw scores to z scores

D. there is no functional means of standardization for the normal curve

16. A z score of 2.5 would indicate what with respect to the raw score’s proximity to the distribution mean?

A. that the raw score lies precisely 2.5 standard deviations above the mean

B. that the distribution has a mean of 2.5

C. that the raw score lies 2.5 standard deviations below the mean

D. that the modal category for the distribution lies 2.5 standard deviations below the mean

17. What is the essential difference between the normal curve and the standard normal curve?

A. The standard normal curve is constructed entirely of transformed percentages, while the normal curve is constructed of raw scores.

B. The normal curve is comprised of transformed percentages, while the standard normal curve is constructed of raw scores.

C. The standard normal curve is comprised of z scores, and the normal curve is constructed of raw scores.

D. There is nothing different between the standard normal curve and the normal curve.

18. The standard normal curve has an area of ______.

A. 1.00

B. 0

C. 0.50

D. 2.00

19. The standard normal curve always has a mean of ______.

A. 1

B. 0

C. −1

D. 2

20. The area under the curve in the standard normal curve represents ______.

A. raw scores

B. proportions and probability

C. correlations

D. frequencies

21. z Scores greater than 1 or less than −1 ______.

A. are typical or “normal” scores and group together close to the distribution mean

B. are relatively rare because they fall one or more standard deviations away from the mean

C. are treated as special cases and used for further correlational analyses

D. fall so far away from the mean of the distribution that they are not placed on the curve itself when conducting statistical analyses

22. What is the basis of inferential statistics?

A. probability

B. percentages

C. correlations

D. means

23. What did Paoline et al. find to be the most consistent predictors of stress and satisfaction in jail security staff in their 2006 study?

A. pay and vacation time

B. clear and fair policies and positive views toward coworkers

C. policies that coincide with officer’s personal beliefs

D. cooperative inmates and positive relationships with coworkers

24. What is at the heart of the binomial probability distribution?

A. proportions

B. the probability of success

C. inferential statistics

D. z scores

25. What formula guarantees that the probability of r successes and N – r failures is the product of p and q?

A. the restricted multiplication rule for independent events

B. the success/failure test

C. the binomial probability test

D. the probability of failure rules

26. In statistics, the symbol ______ indicates to a researcher to multiply a number by every number starting with itself and less one all the way to 1.00.

A. ?

B. !

C. x

D. /

27. Continuous variables are represented by a distribution called the ____________.

A. normal curve

B. abnormal curve

C. oblong curve

D. none of these

28. In terms of shape, the normal curve is ______ and ______.

A. asymmetric; unimodal

B. asymmetric; bimodal

C. symmetric; unimodal

D. symmetric; bimodal

29. A standardized version of a raw score that allows scientists to determine how close the score is to the mean and whether it is greater than or less than the mean is a ______.

A. z score

B. inverted score

C. standard deviation

D. none of these

30. A negative z score would indicate a raw score that lies ______ the mean of the distribution.

A. above

B. below

C. exactly on

D. none of these

31. When all of the raw scores in a distribution have been transformed to z scores and plotted, the result is the ______.

A. standard abnormal curve

B. positively skewed curve

C. standard normal curve

D. negatively skewed curve

32. The area under the standard normal curve, representing the scores falling within 1 standard deviation above the mean, is ______.

A. 0.3413

B. 0.6826

C. 0.7515

D. 0.9616

33. A table containing a list of z scores and the area of the curve that is between the distribution mean and each individual z score is called a ______.

A. t table

B. z table

C. f table

D. none of these

34. The basis of inferential statistics is ___________.

A. probability

B. normality

C. physics

D. none of these

35. ______ distributions are tangible.

A. theoretical

B. empirical

C. metaphorical

D. none of these

1. If a z-score is negative, then the area associated with that score will also be negative.

2. The relationship between theoretical predictions and empirical findings is at the heart of statistical analysis.

3. Researchers are constantly comparing observations to expectations to determine whether empirical outcomes conform to theory-based predictions about those outcomes.

4. Binomials are also referred to as dichotomous or binary.

5. A binomial distribution is constructed using the binomial coefficient.

6. The area of the normal curve is equal to 1.00.

7. The normal curve has two modes.

8. The characteristics that determine a normal curve’s location on the number line and its shape are its mean and standard deviation.

9. There is no exact, predetermined shape to the normal curve as every distribution will have its own unique shape.

10. One nuance of the z score is that it can never take on a negative value.

11. The normal curve is constructed of raw scores whereas the standard normal curve is constructed of z scores.

12. The standard normal curve has a mean of 1 and a standard deviation of 0.

13. The area under the standard normal curve represents proportions and probabilities.

14. While z scores can be used to find areas under the standard normal curve, areas cannot be used to reverse the process and find corresponding z scores.

15. Although z scores can be negative, areas are always positive.

16. A z score is expressed in standard deviation units.

17. In binomials, outcomes other than successes are referred to as failures.

18. A normal distribution is a table or graph showing the full array of theoretical probabilities for any given variable.

19. Binomials are trials that have exactly two possible outcomes.

20. A binomial is a particular act with multiple different possible outcomes.

1. Describe the many unique characteristics of the normal curve.

2. What is a probability?

3. What is the purpose of inferential statistics?

4. What is the fundamental difference between theoretical predictions and empirical outcomes?

5. Transform each of the raw scores in the following hypothetical grade distribution into z scores.

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