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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 result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data
descriptive statistics
Atomic event
Posterior probability
Standard error
2. 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
Statistical inference
Mutual independence
Seasonal effect
Inferential statistics
3. Where the null hypothesis fails to be rejected and an actual difference between populations is missed giving a 'false negative'.
Cumulative distribution functions
Beta value
Lurking variable
Type II errors
4. To find the average - or arithmetic mean - of a set of numbers:
Descriptive statistics
Probability density functions
Correlation coefficient
Divide the sum by the number of values.
5. 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.
Conditional probability
Estimator
Block
hypothesis
6. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively
A statistic
Residuals
Ordinal measurements
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
7. Used to reduce bias - this measure weights the more relevant information higher than less relevant info.
Greek letters
hypotheses
A random variable
Statistical adjustment
8. 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.
descriptive statistics
Sampling frame
A population or statistical population
Correlation coefficient
9. 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
Residuals
Correlation
A likelihood function
P-value
10. When you have two or more competing models - choose the simpler of the two models.
Law of Parsimony
Sampling frame
A data point
That value is the median value
11. A variable describes an individual by placing the individual into a category or a group.
Qualitative variable
Joint distribution
Ratio measurements
Binary data
12. A consistent - repeated deviation of the sample statistic from the population parameter in the same direction when many samples are taken.
Type 1 Error
Dependent Selection
Bias
Power of a test
13. E[X] :
The average - or arithmetic mean
Sampling
Particular realizations of a random variable
expected value of X
14. Gives the probability distribution for a continuous random variable.
A probability density function
Prior probability
A data set
observational study
15. Is a function that gives the probability of all elements in a given space: see List of probability distributions
A statistic
hypothesis
A probability distribution
A probability space
16. A list of individuals from which the sample is actually selected.
Atomic event
Sampling frame
Sampling Distribution
Marginal probability
17. 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
Count data
hypotheses
That is the median value
A sampling distribution
18. A data value that falls outside the overall pattern of the graph.
inferential statistics
A likelihood function
Outlier
Parameter - or 'statistical parameter'
19. A scale that represents an ordinal scale such as looks on a scale from 1 to 10.
Qualitative variable
applied statistics
Kurtosis
Likert scale
20. 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.
An experimental study
nominal - ordinal - interval - and ratio
Sampling frame
expected value of X
21. Many statistical methods seek to minimize the mean-squared error - and these are called
A random variable
methods of least squares
Kurtosis
The sample space
22. Are simply two different terms for the same thing. Add the given values
Average and arithmetic mean
Inferential statistics
hypotheses
hypothesis
23. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
Simulation
Law of Large Numbers
Skewness
observational study
24. Another name for elementary event.
The Expected value
Variability
hypothesis
Atomic event
25. 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).
Observational study
Joint probability
An event
Conditional probability
26. (also called statistical variability) is a measure of how diverse some data is. It can be expressed by the variance or the standard deviation.
Dependent Selection
Ratio measurements
Particular realizations of a random variable
Statistical dispersion
27. 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
Kurtosis
The Covariance between two random variables X and Y - with expected values E(X) =
The median value
28. Statistical methods can be used for summarizing or describing a collection of data; this is called
Statistical dispersion
Descriptive
That is the median value
descriptive statistics
29. Any specific experimental condition applied to the subjects
Standard error
A Probability measure
Treatment
Marginal probability
30. The probability of correctly detecting a false null hypothesis.
Power of a test
nominal - ordinal - interval - and ratio
An estimate of a parameter
A sampling distribution
31. (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.
expected value of X
Type II errors
An Elementary event
Alpha value (Level of Significance)
32. A measure that is relevant or appropriate as a representation of that property.
Inferential statistics
That is the median value
Correlation
Valid measure
33. Is the result of applying a statistical algorithm to a data set. It can also be described as an observable random variable.
A statistic
Observational study
Alpha value (Level of Significance)
A sample
34. A numerical measure that describes an aspect of a population.
Parameter
Law of Large Numbers
Alpha value (Level of Significance)
Prior probability
35. Is the most commonly used measure of statistical dispersion. It is the square root of the variance - and is generally written s (sigma).
Variable
The standard deviation
Correlation
Nominal measurements
36. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.
Descriptive
Step 2 of a statistical experiment
Law of Parsimony
Kurtosis
37. Statistics involve methods of using information from a sample to draw conclusions regarding the population.
An Elementary event
Inferential
Credence
Probability density functions
38. Uses patterns in the sample data to draw inferences about the population represented - accounting for randomness. These inferences may take the form of: answering yes/no questions about the data (hypothesis testing) - estimating numerical characteris
Inferential statistics
A statistic
Probability and statistics
Valid measure
39. Error also refers to the extent to which individual observations in a sample differ from a central value - such as
The Range
Power of a test
the sample or population mean
Beta value
40. Gives the probability of events in a probability space.
A Probability measure
Variable
The Covariance between two random variables X and Y - with expected values E(X) =
the population mean
41. The proportion of the explained variation by a linear regression model in the total variation.
Statistics
Coefficient of determination
applied statistics
Mutual independence
42. 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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43. The standard deviation of a sampling distribution.
f(z) - and its cdf by F(z).
Marginal distribution
The standard deviation
Standard error
44. Some commonly used symbols for sample statistics
Kurtosis
The standard deviation
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Nominal measurements
45. 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
Valid measure
s-algebras
Probability
Conditional probability
46. (pdfs) and probability mass functions are denoted by lower case letters - e.g. f(x).
Law of Parsimony
Step 3 of a statistical experiment
Statistical adjustment
Probability density functions
47. A numerical measure that describes an aspect of a sample.
The Covariance between two random variables X and Y - with expected values E(X) =
hypothesis
A data point
Statistic
48. 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
Descriptive statistics
Seasonal effect
Cumulative distribution functions
Observational study
49. A group of individuals sharing some common features that might affect the treatment.
Block
Lurking variable
Probability density functions
A sampling distribution
50. Are usually written with upper case calligraphic (e.g. F for the set of sets on which we define the probability P)
s-algebras
the population variance
inferential statistics
Simpson's Paradox