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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. A numerical measure that describes an aspect of a sample.
Treatment
That is the median value
Interval measurements
Statistic
2. (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.
An Elementary event
Observational study
Probability density
The sample space
3. Long-term upward or downward movement over time.
Sampling Distribution
A probability distribution
the sample or population mean
Trend
4. When info. in a contingency table is re-organized into more or less categories - relationships seen can change or reverse.
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5. Is a sample and the associated data points.
A data set
Quantitative variable
the population cumulants
A statistic
6. Is a parameter that indexes a family of probability distributions.
Skewness
Random variables
A Statistical parameter
observational study
7. 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
Divide the sum by the number of values.
Conditional distribution
Step 3 of a statistical experiment
Type II errors
8. A list of individuals from which the sample is actually selected.
Sampling frame
Power of a test
Statistical dispersion
An Elementary event
9. Cov[X - Y] :
Credence
descriptive statistics
covariance of X and Y
hypotheses
10. The collection of all possible outcomes in an experiment.
Simulation
Independence or Statistical independence
A probability density function
Sample space
11. (also called statistical variability) is a measure of how diverse some data is. It can be expressed by the variance or the standard deviation.
A Distribution function
Parameter - or 'statistical parameter'
Statistical dispersion
Null hypothesis
12. Is a process of selecting observations to obtain knowledge about a population. There are many methods to choose on which sample to do the observations.
Confounded variables
Sampling
Greek letters
Nominal measurements
13. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
applied statistics
Correlation coefficient
Pairwise independence
Bias
14. (or multivariate random variable) is a vector whose components are random variables on the same probability space.
A Random vector
Step 3 of a statistical experiment
Experimental and observational studies
Divide the sum by the number of values.
15. A variable describes an individual by placing the individual into a category or a group.
s-algebras
An estimate of a parameter
Qualitative variable
Count data
16. The result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data
The Mean of a random variable
A likelihood function
Power of a test
Posterior probability
17. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.
An estimate of a parameter
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Type II errors
Nominal measurements
18. Is that part of a population which is actually observed.
Correlation coefficient
A sample
Outlier
The Mean of a random variable
19. S^2
Prior probability
the population variance
Statistics
Ordinal measurements
20. To find the median value of a set of numbers: Arrange the numbers in numerical order. Locate the two middle numbers in the list. Find the average of those two middle values.
applied statistics
Inferential statistics
Probability and statistics
That value is the median value
21. Is a function that gives the probability of all elements in a given space: see List of probability distributions
Simulation
A probability distribution
Residuals
A data set
22. Used to reduce bias - this measure weights the more relevant information higher than less relevant info.
Correlation coefficient
Statistical adjustment
Statistical inference
Alpha value (Level of Significance)
23. 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 I errors & Type II errors
A sample
Probability
Power of a test
24. Have no meaningful rank order among values.
A random variable
Nominal measurements
Seasonal effect
Statistical inference
25. A collection of events is mutually independent if for any subset of the collection - the joint probability of all events occurring is equal to the product of the joint probabilities of the individual events. Think of the result of a series of coin-fl
Law of Large Numbers
methods of least squares
Random variables
Mutual independence
26. 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
Dependent Selection
Statistic
hypotheses
Variability
27. When there is an even number of values...
the population cumulants
That is the median value
Step 3 of a statistical experiment
Standard error
28. A measure that is relevant or appropriate as a representation of that property.
Valid measure
Correlation
A probability density function
Prior probability
29. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
Step 2 of a statistical experiment
P-value
Statistical dispersion
Step 3 of a statistical experiment
30. Summarize the population data by describing what was observed in the sample numerically or graphically. Numerical descriptors include mean and standard deviation for continuous data types (like heights or weights) - while frequency and percentage are
Observational study
Power of a test
Independent Selection
Descriptive statistics
31. 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.
Joint distribution
A Distribution function
Sampling Distribution
An experimental study
32. E[X] :
Dependent Selection
nominal - ordinal - interval - and ratio
Outlier
expected value of X
33. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
Prior probability
Probability
Lurking variable
Probability density
34. Are simply two different terms for the same thing. Add the given values
A data point
Average and arithmetic mean
Atomic event
A sample
35. 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
Null hypothesis
Step 2 of a statistical experiment
Standard error
A probability density function
36. Is data that can take only two values - usually represented by 0 and 1.
Pairwise independence
The average - or arithmetic mean
Binary data
Ratio measurements
37. Ratio and interval measurements which can be either discrete or continuous - due to their numerical nature are grouped together as
Statistical inference
quantitative variables
the population correlation
Type I errors & Type II errors
38. 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.
Bias
Independent Selection
Parameter - or 'statistical parameter'
Coefficient of determination
39. Given two random variables X and Y - the joint distribution of X and Y is the probability distribution of X and Y together.
Standard error
Treatment
A statistic
Joint distribution
40. In particular - the pdf of the standard normal distribution is denoted by
f(z) - and its cdf by F(z).
the population mean
A Statistical parameter
An experimental study
41. 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.
the population cumulants
hypotheses
experimental studies and observational studies.
Marginal distribution
42. A subjective estimate of probability.
A Distribution function
Nominal measurements
Credence
Variability
43. (e.g. ? - b) are commonly used to denote unknown parameters (population parameters).
The Range
Experimental and observational studies
Greek letters
Statistical inference
44. Where the null hypothesis fails to be rejected and an actual difference between populations is missed giving a 'false negative'.
The standard deviation
Type II errors
f(z) - and its cdf by F(z).
Statistical dispersion
45. Given two jointly distributed random variables X and Y - the conditional probability distribution of Y given X (written 'Y | X') is the probability distribution of Y when X is known to be a particular value.
Type II errors
the population variance
The Range
Conditional distribution
46. 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.
Residuals
Credence
Bias
Count data
47. 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.
Posterior probability
f(z) - and its cdf by F(z).
A Distribution function
Marginal probability
48. 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.
Statistics
Type 1 Error
Dependent Selection
The sample space
49. 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
inferential statistics
Descriptive statistics
the population correlation
Parameter - or 'statistical parameter'
50. Is a sample space over which a probability measure has been defined.
A probability space
Inferential statistics
Type I errors
the population mean