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Test your basic knowledge |
CLEP General Mathematics: Probability And Statistics
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clep
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math
Instructions:
Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.
This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.
1. Statistics involve methods of using information from a sample to draw conclusions regarding the population.
descriptive statistics
Inferential
Correlation
quantitative variables
2. Is data arising from counting that can take only non-negative integer values.
Count data
The average - or arithmetic mean
Bias
Law of Large Numbers
3. Of a group of numbers is the center point of all those number values.
The average - or arithmetic mean
Marginal distribution
Sample space
quantitative variables
4. Are usually written with upper case calligraphic (e.g. F for the set of sets on which we define the probability P)
experimental studies and observational studies.
the population variance
Average and arithmetic mean
s-algebras
5. In particular - the pdf of the standard normal distribution is denoted by
variance of X
Individual
That value is the median value
f(z) - and its cdf by F(z).
6. Describes the spread in the values of the sample statistic when many samples are taken.
Variability
Probability density
Correlation
Quantitative variable
7. Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically - sometimes they are grouped together as
Sample space
categorical variables
Particular realizations of a random variable
Probability density
8. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
Pairwise independence
An experimental study
A Random vector
Posterior probability
9. Is the study of the collection - organization - analysis - and interpretation of data. It deals with all aspects of this - including the planning of data collection in terms of the design of surveys and experiments.
covariance of X and Y
Probability density
Statistics
Sampling Distribution
10. Any specific experimental condition applied to the subjects
Estimator
The Range
Treatment
Statistical inference
11. Design of experiments - using blocking to reduce the influence of confounding variables - and randomized assignment of treatments to subjects to allow unbiased estimates of treatment effects and experimental error. At this stage - the experimenters a
A data point
Step 2 of a statistical experiment
Statistical inference
Bias
12. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively
The Range
Standard error
Residuals
Skewness
13. Gives the probability distribution for a continuous random variable.
Binary data
Posterior probability
A probability density function
Credence
14. Can be a population parameter - a distribution parameter - an unobserved parameter (with different shades of meaning). In statistics - this is often a quantity to be estimated.
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15. The objects described by a set of data: person (animal) - place - and - thing. (SUBJECTS)
P-value
Individual
A data set
Probability density
16. Is a sample and the associated data points.
Statistical inference
A data set
That value is the median value
Descriptive
17. A numerical facsimilie or representation of a real-world phenomenon.
Correlation coefficient
Step 1 of a statistical experiment
Simulation
Conditional probability
18. A data value that falls outside the overall pattern of the graph.
quantitative variables
hypothesis
A probability distribution
Outlier
19. Are two related but separate academic disciplines. Statistical analysis often uses probability distributions - and the two topics are often studied together. However - probability theory contains much that is of mostly of mathematical interest and no
Probability and statistics
A Random vector
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Beta value
20. A numerical measure that describes an aspect of a population.
nominal - ordinal - interval - and ratio
Parameter
An Elementary event
The standard deviation
21. Is the probability of an event - ignoring any information about other events. The marginal probability of A is written P(A). Contrast with conditional probability.
Marginal probability
Divide the sum by the number of values.
Random variables
Sampling
22. Is used in 'mathematical statistics' (alternatively - 'statistical theory') to study the sampling distributions of sample statistics and - more generally - the properties of statistical procedures. The use of any statistical method is valid when the
Probability
A Random vector
Correlation coefficient
The Range
23. The probability of correctly detecting a false null hypothesis.
hypothesis
Credence
the population cumulants
Power of a test
24. Is a measure of the asymmetry of the probability distribution of a real-valued random variable. Roughly speaking - a distribution has positive skew (right-skewed) if the higher tail is longer and negative skew (left-skewed) if the lower tail is longe
Skewness
Average and arithmetic mean
Binomial experiment
Block
25. Two variables such that their effects on the response variable cannot be distinguished from each other.
Confounded variables
Posterior probability
Sampling frame
Statistical dispersion
26. A scale that represents an ordinal scale such as looks on a scale from 1 to 10.
Individual
Simulation
Likert scale
The average - or arithmetic mean
27. ?
the population correlation
Particular realizations of a random variable
Confounded variables
Probability
28. Probability of rejecting a true null hypothesis.
methods of least squares
Alpha value (Level of Significance)
The Mean of a random variable
hypotheses
29. Is the exact middle value of a set of numbers Arrange the numbers in numerical order. Find the value in the middle of the list.
Simulation
The median value
The Range
Inferential statistics
30. Some commonly used symbols for population parameters
A probability space
Atomic event
Binary data
the population mean
31. Performing the experiment following the experimental protocol and analyzing the data following the experimental protocol. 4. Further examining the data set in secondary analyses - to suggest new hypotheses for future study. 5. Documenting and present
Pairwise independence
Prior probability
Step 3 of a statistical experiment
Quantitative variable
32. Can be - for example - the possible outcomes of a dice roll (but it is not assigned a value). The distribution function of a random variable gives the probability of different results. We can also derive the mean and variance of a random variable.
An event
A random variable
Law of Large Numbers
An experimental study
33. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
nominal - ordinal - interval - and ratio
Block
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Observational study
34. Is the result of applying a statistical algorithm to a data set. It can also be described as an observable random variable.
f(z) - and its cdf by F(z).
A statistic
Seasonal effect
A random variable
35. There are two major types of causal statistical studies: In both types of studies - the effect of differences of an independent variable (or variables) on the behavior of the dependent variable are observed. The difference between the two types lies
Type 2 Error
Lurking variable
experimental studies and observational studies.
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
36. Given two jointly distributed random variables X and Y - the marginal distribution of X is simply the probability distribution of X ignoring information about Y.
Marginal distribution
Conditional distribution
Type 2 Error
Particular realizations of a random variable
37. Where the null hypothesis fails to be rejected and an actual difference between populations is missed giving a 'false negative'.
Type II errors
Binary data
Statistic
Type 1 Error
38. Is its expected value. The mean (or sample mean of a data set is just the average value.
The Mean of a random variable
Individual
Binomial experiment
Quantitative variable
39. Some commonly used symbols for sample statistics
Variability
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Law of Parsimony
Conditional distribution
40. (or atomic event) is an event with only one element. For example - when pulling a card out of a deck - 'getting the jack of spades' is an elementary event - while 'getting a king or an ace' is not.
Statistical inference
Statistic
Qualitative variable
An Elementary event
41.
the population mean
Confounded variables
Sample space
Greek letters
42. The standard deviation of a sampling distribution.
Estimator
Statistic
Standard error
The average - or arithmetic mean
43. Is the function that gives the probability distribution of a random variable. It cannot be negative - and its integral on the probability space is equal to 1.
Joint distribution
Sample space
A Distribution function
Beta value
44. The result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data
Statistical adjustment
A Probability measure
The Range
Posterior probability
45. A list of individuals from which the sample is actually selected.
Sampling frame
f(z) - and its cdf by F(z).
That value is the median value
Statistic
46. Samples are drawn from two different populations such that the sample data drawn from one population is completely unrelated to the selection of sample data from the other population.
Coefficient of determination
inferential statistics
Posterior probability
Independent Selection
47. Working from a null hypothesis two basic forms of error are recognized:
Probability
Type I errors & Type II errors
Law of Large Numbers
inferential statistics
48. Involves taking measurements of the system under study - manipulating the system - and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements.
Step 2 of a statistical experiment
methods of least squares
An experimental study
observational study
49. Can refer either to a sample not being representative of the population - or to the difference between the expected value of an estimator and the true value.
Random variables
Simulation
Bias
The sample space
50. Is a subset of the sample space - to which a probability can be assigned. For example - on rolling a die - 'getting a five or a six' is an event (with a probability of one third if the die is fair).
Sampling
A data point
Average and arithmetic mean
An event