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CLEP General Mathematics: Probability And Statistics
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clep
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Instructions:
Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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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
A sampling distribution
Sampling
Lurking variable
2. A numerical measure that describes an aspect of a sample.
A population or statistical population
Type 1 Error
Statistic
Type I errors & Type II errors
3. Are usually written in upper case roman letters: X - Y - etc.
An Elementary event
Binary data
The sample space
Random variables
4. 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
Observational study
Beta value
Probability and statistics
f(z) - and its cdf by F(z).
5. A numerical measure that describes an aspect of a population.
Probability density functions
A statistic
Parameter
A random variable
6. A variable has a value or numerical measurement for which operations such as addition or averaging make sense.
Bias
Reliable measure
Marginal distribution
Quantitative variable
7. 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.
Trend
Type 1 Error
Treatment
A data point
8. 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
Step 1 of a statistical experiment
Probability
Statistical dispersion
Ordinal measurements
9. 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.
Simple random sample
Sampling
A population or statistical population
Mutual independence
10. 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
Average and arithmetic mean
Skewness
Estimator
A population or statistical population
11. Have imprecise differences between consecutive values - but have a meaningful order to those values
Ordinal measurements
Average and arithmetic mean
The standard deviation
Statistics
12. The result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data
Sampling
Posterior probability
Probability density functions
the population mean
13. A numerical facsimilie or representation of a real-world phenomenon.
Sampling Distribution
A data point
Simulation
The sample space
14. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
The Range
Interval measurements
Residuals
Prior probability
15. Are written in corresponding lower case letters. For example x1 - x2 - ... - xn could be a sample corresponding to the random variable X.
Sampling frame
A likelihood function
Particular realizations of a random variable
s-algebras
16. 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.
experimental studies and observational studies.
Statistical inference
Skewness
Average and arithmetic mean
17. Is the length of the smallest interval which contains all the data.
Sampling frame
Bias
The Range
Interval measurements
18. 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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19. Samples are drawn from two different populations such that there is a matching of the first sample data drawn and a corresponding data value in the second sample data.
A sample
A probability space
That is the median value
Dependent Selection
20. Occurs when a subject receives no treatment - but (incorrectly) believes he or she is in fact receiving treatment and responds favorably.
Independence or Statistical independence
Divide the sum by the number of values.
Type I errors & Type II errors
Placebo effect
21. Two variables such that their effects on the response variable cannot be distinguished from each other.
Random variables
The median value
Confounded variables
Binary data
22. 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
Step 3 of a statistical experiment
Greek letters
Statistic
Descriptive statistics
23. 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
A Distribution function
hypothesis
Null hypothesis
Individual
24. (also called statistical variability) is a measure of how diverse some data is. It can be expressed by the variance or the standard deviation.
Parameter
Statistical dispersion
The Expected value
expected value of X
25. When info. in a contingency table is re-organized into more or less categories - relationships seen can change or reverse.
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26. Many statistical methods seek to minimize the mean-squared error - and these are called
A probability space
methods of least squares
Probability
applied statistics
27. A measure that is relevant or appropriate as a representation of that property.
Credence
Seasonal effect
Valid measure
Posterior probability
28. Some commonly used symbols for population parameters
the population mean
Sampling Distribution
Interval measurements
Valid measure
29. 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.
A Random vector
Particular realizations of a random variable
Sampling
Likert scale
30. The objects described by a set of data: person (animal) - place - and - thing. (SUBJECTS)
Bias
the population mean
Law of Large Numbers
Individual
31. Is a sample and the associated data points.
An Elementary event
A data set
Sampling
hypotheses
32. Is used to describe probability in a continuous probability distribution. For example - you can't say that the probability of a man being six feet tall is 20% - but you can say he has 20% of chances of being between five and six feet tall. Probabilit
variance of X
Probability density
A sampling distribution
The median value
33. 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
observational study
Nominal measurements
Independence or Statistical independence
Standard error
34. Changes over time that show a regular periodicity in the data where regular means over a fixed interval; the time between repetitions is called the period.
That is the median value
Seasonal effect
Outlier
P-value
35. When there is an even number of values...
Posterior probability
Qualitative variable
Estimator
That is the median value
36. Is defined as the expected value of random variable (X -
Interval measurements
methods of least squares
A sample
The Covariance between two random variables X and Y - with expected values E(X) =
37. 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.
Sample space
Greek letters
Simple random sample
Null hypothesis
38. Is a function that gives the probability of all elements in a given space: see List of probability distributions
expected value of X
descriptive statistics
A probability distribution
Ratio measurements
39. (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.
Binomial experiment
An Elementary event
Average and arithmetic mean
Simulation
40. Where the null hypothesis fails to be rejected and an actual difference between populations is missed giving a 'false negative'.
Type II errors
A Random vector
Count data
Credence
41. 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.
Likert scale
Descriptive
Estimator
hypothesis
42. Probability of accepting a false null hypothesis.
Prior probability
Parameter
Beta value
Outlier
43. 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.
Coefficient of determination
Nominal measurements
The variance of a random variable
nominal - ordinal - interval - and ratio
44. 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.
Type I errors & Type II errors
Alpha value (Level of Significance)
Cumulative distribution functions
Kurtosis
45. (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
A probability density function
A statistic
Step 3 of a statistical experiment
A likelihood function
46. Describes the spread in the values of the sample statistic when many samples are taken.
A data set
expected value of X
Variability
Joint distribution
47. Are usually written with upper case calligraphic (e.g. F for the set of sets on which we define the probability P)
s-algebras
Joint distribution
Likert scale
Independence or Statistical independence
48. The probability of correctly detecting a false null hypothesis.
Simpson's Paradox
Type I errors & Type II errors
Power of a test
That is the median value
49. (or multivariate random variable) is a vector whose components are random variables on the same probability space.
Probability density functions
Variable
Sampling
A Random vector
50. The standard deviation of a sampling distribution.
Probability density functions
The variance of a random variable
Seasonal effect
Standard error
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