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Test your basic knowledge |
CLEP General Mathematics: Probability And Statistics
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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. Is a sample space over which a probability measure has been defined.
Qualitative variable
inferential statistics
A probability space
Conditional distribution
2. 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.
Simpson's Paradox
Step 3 of a statistical experiment
The variance of a random variable
Individual
3. Describes the spread in the values of the sample statistic when many samples are taken.
Variability
Probability and statistics
Alpha value (Level of Significance)
Ordinal measurements
4. Var[X] :
A Probability measure
Type II errors
A Distribution function
variance of X
5. Gives the probability distribution for a continuous random variable.
Estimator
Treatment
A probability density function
Probability density functions
6. Is inference about a population from a random sample drawn from it or - more generally - about a random process from its observed behavior during a finite period of time.
Sample space
Statistical inference
Simpson's Paradox
the population variance
7. Long-term upward or downward movement over time.
Trend
Independence or Statistical independence
Qualitative variable
Law of Large Numbers
8. Error also refers to the extent to which individual observations in a sample differ from a central value - such as
Interval measurements
Joint probability
the sample or population mean
Parameter
9. 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.
Step 2 of a statistical experiment
Inferential statistics
Statistical adjustment
Estimator
10. 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
Joint distribution
Step 2 of a statistical experiment
A random variable
An event
11. A measurement such that the random error is small
Likert scale
Reliable measure
expected value of X
Type 2 Error
12. Many statistical methods seek to minimize the mean-squared error - and these are called
methods of least squares
Correlation coefficient
applied statistics
A probability distribution
13. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
The Range
Correlation
P-value
Marginal distribution
14. 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.
A population or statistical population
hypothesis
Residuals
Statistics
15. Any specific experimental condition applied to the subjects
Law of Large Numbers
Mutual independence
Treatment
The Range
16. Is that part of a population which is actually observed.
inferential statistics
A sample
Type II errors
Binomial experiment
17. Another name for elementary event.
Placebo effect
Seasonal effect
s-algebras
Atomic event
18. (pdfs) and probability mass functions are denoted by lower case letters - e.g. f(x).
A probability space
A random variable
Probability density functions
A Random vector
19. Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically - sometimes they are grouped together as
the population correlation
A sampling distribution
categorical variables
observational study
20. Have no meaningful rank order among values.
Probability and statistics
Nominal measurements
Trend
Conditional probability
21. A scale that represents an ordinal scale such as looks on a scale from 1 to 10.
expected value of X
Treatment
Statistic
Likert scale
22. Cov[X - Y] :
inferential statistics
covariance of X and Y
An experimental study
Step 1 of a statistical experiment
23. Gives the probability of events in a probability space.
Simpson's Paradox
Statistical dispersion
Outlier
A Probability measure
24. Is a parameter that indexes a family of probability distributions.
A Statistical parameter
Nominal measurements
Step 2 of a statistical experiment
The median value
25. Have imprecise differences between consecutive values - but have a meaningful order to those values
Average and arithmetic mean
Ordinal measurements
Conditional distribution
s-algebras
26. 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
Mutual independence
the population cumulants
the population correlation
27. Two events are independent if the outcome of one does not affect that of the other (for example - getting a 1 on one die roll does not affect the probability of getting a 1 on a second roll). Similarly - when we assert that two random variables are i
the population variance
Independence or Statistical independence
inferential statistics
The Covariance between two random variables X and Y - with expected values E(X) =
28. Probability of accepting a false null hypothesis.
Probability and statistics
A Random vector
Beta value
Random variables
29. 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
the population mean
Type II errors
Inferential statistics
Simulation
30. Is defined as the expected value of random variable (X -
The sample space
Probability
Beta value
The Covariance between two random variables X and Y - with expected values E(X) =
31. Is a measure of the 'peakedness' of the probability distribution of a real-valued random variable. Higher kurtosis means more of the variance is due to infrequent extreme deviations - as opposed to frequent modestly sized deviations.
Greek letters
Kurtosis
Mutual independence
Residuals
32. Is the set of possible outcomes of an experiment. For example - the sample space for rolling a six-sided die will be {1 - 2 - 3 - 4 - 5 - 6}.
the population cumulants
descriptive statistics
The sample space
Simple random sample
33. Failing to reject a false null hypothesis.
A statistic
An Elementary event
Type 2 Error
the sample or population mean
34. Is its expected value. The mean (or sample mean of a data set is just the average value.
The Mean of a random variable
Outlier
The standard deviation
Inferential
35. 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.
experimental studies and observational studies.
Law of Large Numbers
Sampling Distribution
A Distribution function
36. Ratio and interval measurements which can be either discrete or continuous - due to their numerical nature are grouped together as
Cumulative distribution functions
the population cumulants
quantitative variables
Alpha value (Level of Significance)
37. Is a function that gives the probability of all elements in a given space: see List of probability distributions
Credence
Independence or Statistical independence
A probability distribution
Probability and statistics
38. (also called statistical variability) is a measure of how diverse some data is. It can be expressed by the variance or the standard deviation.
Experimental and observational studies
P-value
Statistical dispersion
Conditional probability
39. (cdfs) are denoted by upper case letters - e.g. F(x).
Block
Beta value
A likelihood function
Cumulative distribution functions
40. (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
Prior probability
Standard error
Step 3 of a statistical experiment
A likelihood function
41. Is one that explores the correlation between smoking and lung cancer. This type of study typically uses a survey to collect observations about the area of interest and then performs statistical analysis. In this case - the researchers would collect o
Probability density
Block
Observational study
An event
42. A consistent - repeated deviation of the sample statistic from the population parameter in the same direction when many samples are taken.
Average and arithmetic mean
Bias
An Elementary event
An event
43. 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
Conditional distribution
A statistic
f(z) - and its cdf by F(z).
44. A data value that falls outside the overall pattern of the graph.
The average - or arithmetic mean
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Outlier
Independent Selection
45. 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.
A statistic
hypotheses
The median value
Sampling
46. Where the null hypothesis is falsely rejected giving a 'false positive'.
A Distribution function
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Treatment
Type I errors
47. 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.
A Probability measure
Step 3 of a statistical experiment
Quantitative variable
48. Consists of a number of independent trials repeated under identical conditions. On each trial - there are two possible outcomes.
That is the median value
Binomial experiment
Parameter
A Probability measure
49. 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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50. 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
The average - or arithmetic mean
Probability density
Bias
Skewness