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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.
If you are not ready to take this test, you can
study here
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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. The proportion of the explained variation by a linear regression model in the total variation.
An experimental study
Coefficient of determination
Cumulative distribution functions
A sampling distribution
2. 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.
Treatment
An experimental study
nominal - ordinal - interval - and ratio
Type 1 Error
3. The standard deviation of a sampling distribution.
Step 2 of a statistical experiment
Standard error
A probability distribution
Ratio measurements
4. (cdfs) are denoted by upper case letters - e.g. F(x).
Cumulative distribution functions
Type I errors
An estimate of a parameter
Variability
5. Occurs when a subject receives no treatment - but (incorrectly) believes he or she is in fact receiving treatment and responds favorably.
Placebo effect
Correlation
Greek letters
Skewness
6. A numerical measure that describes an aspect of a sample.
Random variables
applied statistics
Statistic
Standard error
7. Cov[X - Y] :
f(z) - and its cdf by F(z).
covariance of X and Y
Quantitative variable
An event
8. A variable has a value or numerical measurement for which operations such as addition or averaging make sense.
Valid measure
Nominal measurements
Quantitative variable
Null hypothesis
9. In number theory - scatter plots of data generated by a distribution function may be transformed with familiar tools used in statistics to reveal underlying patterns - which may then lead to
hypotheses
A likelihood function
A Probability measure
An experimental study
10. (or multivariate random variable) is a vector whose components are random variables on the same probability space.
A Random vector
Particular realizations of a random variable
The sample space
Kurtosis
11. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
An event
Individual
A probability space
nominal - ordinal - interval - and ratio
12. The result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data
That is the median value
Posterior probability
Observational study
expected value of X
13. 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
Type 1 Error
experimental studies and observational studies.
Probability
Average and arithmetic mean
14. 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
Reliable measure
Step 3 of a statistical experiment
Beta value
Parameter - or 'statistical parameter'
15. (or just likelihood) is a conditional probability function considered a function of its second argument with its first argument held fixed. For example - imagine pulling a numbered ball with the number k from a bag of n balls - numbered 1 to n. Then
Binary data
Ordinal measurements
Seasonal effect
A likelihood function
16.
A Statistical parameter
A statistic
the population mean
Conditional distribution
17. Is the probability distribution - under repeated sampling of the population - of a given statistic.
Qualitative variable
A sampling distribution
hypothesis
Coefficient of determination
18. Long-term upward or downward movement over time.
Statistical inference
A population or statistical population
Greek letters
Trend
19. Is a function of the known data that is used to estimate an unknown parameter; an estimate is the result from the actual application of the function to a particular set of data. The mean can be used as an estimator.
The Range
Estimator
nominal - ordinal - interval - and ratio
Probability density functions
20. 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.
the population variance
Residuals
Statistics
Credence
21. Is data that can take only two values - usually represented by 0 and 1.
Binary data
Individual
Inferential statistics
A Distribution function
22. Probability of rejecting a true null hypothesis.
Divide the sum by the number of values.
An event
Descriptive
Alpha value (Level of Significance)
23. 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
A statistic
Individual
The sample space
Skewness
24. Is a set of entities about which statistical inferences are to be drawn - often based on random sampling. One can also talk about a population of measurements or values.
A population or statistical population
applied statistics
Simpson's Paradox
nominal - ordinal - interval - and ratio
25. Data are gathered and correlations between predictors and response are investigated.
Lurking variable
observational study
Placebo effect
The standard deviation
26. Used to reduce bias - this measure weights the more relevant information higher than less relevant info.
Statistical adjustment
Statistic
A data set
Bias
27. Interpretation of statistical information in that the assumption is that whatever is proposed as a cause has no effect on the variable being measured can often involve the development of a
The Covariance between two random variables X and Y - with expected values E(X) =
Atomic event
Null hypothesis
Prior probability
28. Two variables such that their effects on the response variable cannot be distinguished from each other.
Count data
A probability distribution
hypothesis
Confounded variables
29. Is a typed measurement - it can be a boolean value - a real number - a vector (in which case it's also called a data vector) - etc.
Power of a test
A data point
Descriptive
P-value
30. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.
The sample space
Descriptive
Probability density
Random variables
31. Patterns in the data may be modeled in a way that accounts for randomness and uncertainty in the observations - and are then used for drawing inferences about the process or population being studied; this is called
A sampling distribution
inferential statistics
Variable
Posterior probability
32. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
Variable
Random variables
Pairwise independence
The standard deviation
33. Gives the probability of events in a probability space.
Reliable measure
Step 2 of a statistical experiment
A Probability measure
Qualitative variable
34. (or expectation) of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by its payoff ('value'). Thus - it represents the average amount one 'expects' to win per bet if bets with identical odds are re
experimental studies and observational studies.
The Expected value
Statistical dispersion
Lurking variable
35. The objects described by a set of data: person (animal) - place - and - thing. (SUBJECTS)
Individual
Type 2 Error
Count data
Experimental and observational studies
36. 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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37. When info. in a contingency table is re-organized into more or less categories - relationships seen can change or reverse.
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38. Is a measure of its statistical dispersion - indicating how far from the expected value its values typically are. The variance of random variable X is typically designated as - - or simply s2.
Descriptive statistics
Simulation
Sampling
The variance of a random variable
39. Is the probability of two events occurring together. The joint probability of A and B is written P(A and B) or P(A - B).
s-algebras
An Elementary event
A sampling distribution
Joint probability
40. Is defined as the expected value of random variable (X -
Sampling Distribution
Interval measurements
Observational study
The Covariance between two random variables X and Y - with expected values E(X) =
41. Are usually written in upper case roman letters: X - Y - etc.
Random variables
f(z) - and its cdf by F(z).
hypothesis
That is the median value
42. Another name for elementary event.
Statistical inference
Posterior probability
Atomic event
Block
43. A sample selected in such a way that each individual is equally likely to be selected as well as any group of size n is equally likely to be selected.
Valid measure
Simple random sample
The Range
hypotheses
44. (e.g. ? - b) are commonly used to denote unknown parameters (population parameters).
Type 2 Error
Marginal probability
Correlation
Greek letters
45. Also called correlation coefficient - is a numeric measure of the strength of linear relationship between two random variables (one can use it to quantify - for example - how shoe size and height are correlated in the population). An example is the P
Posterior probability
The Range
Probability density
Correlation
46. Rejecting a true null hypothesis.
An Elementary event
Type 1 Error
Step 1 of a statistical experiment
Power of a test
47. Many statistical methods seek to minimize the mean-squared error - and these are called
Type I errors & Type II errors
Count data
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
methods of least squares
48. Is a parameter that indexes a family of probability distributions.
Step 1 of a statistical experiment
expected value of X
Sampling Distribution
A Statistical parameter
49. 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.
Independent Selection
An event
A population or statistical population
The Covariance between two random variables X and Y - with expected values E(X) =
50. Have both a meaningful zero value and the distances between different measurements defined; they provide the greatest flexibility in statistical methods that can be used for analyzing the data
Valid measure
quantitative variables
Block
Ratio measurements