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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. Given two random variables X and Y - the joint distribution of X and Y is the probability distribution of X and Y together.
Joint distribution
the population correlation
Statistics
A sampling distribution
2. Occurs when a subject receives no treatment - but (incorrectly) believes he or she is in fact receiving treatment and responds favorably.
categorical variables
Step 3 of a statistical experiment
Placebo effect
The Mean of a random variable
3. Gives the probability of events in a probability space.
f(z) - and its cdf by F(z).
Interval measurements
A Probability measure
Treatment
4. 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.
That value is the median value
A random variable
Seasonal effect
Step 1 of a statistical experiment
5.
Confounded variables
Interval measurements
the population mean
The Covariance between two random variables X and Y - with expected values E(X) =
6. 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
Alpha value (Level of Significance)
hypotheses
the population variance
Parameter
7. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.
That value is the median value
An estimate of a parameter
Prior probability
Interval measurements
8. Describes a characteristic of an individual to be measured or observed.
Qualitative variable
Greek letters
Law of Large Numbers
Variable
9. The objects described by a set of data: person (animal) - place - and - thing. (SUBJECTS)
Marginal probability
Skewness
Individual
Lurking variable
10. Descriptive statistics and inferential statistics (a.k.a. - predictive statistics) together comprise
Sample space
The Range
Statistical dispersion
applied statistics
11. A numerical measure that describes an aspect of a sample.
the population mean
Interval measurements
Statistic
Qualitative variable
12. The collection of all possible outcomes in an experiment.
nominal - ordinal - interval - and ratio
Sample space
Probability
Variability
13. Are written in corresponding lower case letters. For example x1 - x2 - ... - xn could be a sample corresponding to the random variable X.
Inferential statistics
Descriptive
Particular realizations of a random variable
The Covariance between two random variables X and Y - with expected values E(X) =
14. Var[X] :
Statistical dispersion
variance of X
Statistic
Statistical inference
15. 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 average - or arithmetic mean
A probability distribution
Inferential statistics
variance of X
16. Gives the probability distribution for a continuous random variable.
Statistical adjustment
A probability density function
the population mean
Null hypothesis
17. Many statistical methods seek to minimize the mean-squared error - and these are called
methods of least squares
quantitative variables
Independence or Statistical independence
Atomic event
18. When info. in a contingency table is re-organized into more or less categories - relationships seen can change or reverse.
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19. (also called statistical variability) is a measure of how diverse some data is. It can be expressed by the variance or the standard deviation.
Statistical dispersion
Correlation
Trend
Step 2 of a statistical experiment
20. The result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data
P-value
Posterior probability
That value is the median value
Coefficient of determination
21. 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
The Expected value
Correlation
the population variance
22. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
Experimental and observational studies
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
nominal - ordinal - interval - and ratio
hypothesis
23. Long-term upward or downward movement over time.
Probability density
methods of least squares
Valid measure
Trend
24. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.
An event
Descriptive
The Covariance between two random variables X and Y - with expected values E(X) =
observational study
25. A consistent - repeated deviation of the sample statistic from the population parameter in the same direction when many samples are taken.
An Elementary event
inferential statistics
Probability density
Bias
26. Cov[X - Y] :
nominal - ordinal - interval - and ratio
Mutual independence
Estimator
covariance of X and Y
27. 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.
Simple random sample
Estimator
A statistic
descriptive statistics
28. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
descriptive statistics
Law of Large Numbers
Placebo effect
The Mean of a random variable
29. Are usually written in upper case roman letters: X - Y - etc.
Random variables
Variability
Step 2 of a statistical experiment
descriptive statistics
30. 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 variance
Simple random sample
The sample space
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
31. Error also refers to the extent to which individual observations in a sample differ from a central value - such as
the sample or population mean
A likelihood function
Conditional distribution
Greek letters
32. Is the probability distribution - under repeated sampling of the population - of a given statistic.
P-value
Seasonal effect
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
A sampling distribution
33. 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 Probability measure
Independent Selection
hypotheses
34. (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
Statistical dispersion
A likelihood function
Marginal probability
Type I errors & Type II errors
35. 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.
The Range
covariance of X and Y
Kurtosis
Type I errors & Type II errors
36. 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.
A random variable
Ratio measurements
Inferential
Quantitative variable
37. When there is an even number of values...
Posterior probability
Type I errors
A population or statistical population
That is the median value
38. Describes the spread in the values of the sample statistic when many samples are taken.
Statistical adjustment
Law of Parsimony
Variability
Simpson's Paradox
39. In particular - the pdf of the standard normal distribution is denoted by
Average and arithmetic mean
Independence or Statistical independence
f(z) - and its cdf by F(z).
A Distribution function
40. 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
Conditional distribution
Probability density
Step 2 of a statistical experiment
The Range
41. 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.
The variance of a random variable
Statistical adjustment
Conditional probability
s-algebras
42. Have no meaningful rank order among values.
Experimental and observational studies
Pairwise independence
Interval measurements
Nominal measurements
43. Rejecting a true null hypothesis.
Coefficient of determination
Type 1 Error
Sampling Distribution
Ordinal measurements
44. 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
Null hypothesis
Ordinal measurements
The Expected value
Dependent Selection
45. 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.
The sample space
Independence or Statistical independence
Treatment
Statistical inference
46. 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.
Lurking variable
Statistics
the population mean
Step 2 of a statistical experiment
47. (pdfs) and probability mass functions are denoted by lower case letters - e.g. f(x).
Probability density functions
The variance of a random variable
methods of least squares
Bias
48. Is the most commonly used measure of statistical dispersion. It is the square root of the variance - and is generally written s (sigma).
Step 1 of a statistical experiment
Type II errors
the population mean
The standard deviation
49. 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.
Simpson's Paradox
Simple random sample
The Covariance between two random variables X and Y - with expected values E(X) =
An Elementary event
50. Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically - sometimes they are grouped together as
Credence
Step 1 of a statistical experiment
Valid measure
categorical variables
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