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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.
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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. Are usually written in upper case roman letters: X - Y - etc.
Random variables
applied statistics
Observational study
Marginal probability
2. S^2
Greek letters
P-value
the population variance
The median value
3. Given two random variables X and Y - the joint distribution of X and Y is the probability distribution of X and Y together.
Type I errors & Type II errors
Nominal measurements
Joint distribution
Step 3 of a statistical experiment
4. When you have two or more competing models - choose the simpler of the two models.
Ordinal measurements
Law of Parsimony
descriptive statistics
Marginal distribution
5. Long-term upward or downward movement over time.
Trend
Beta value
observational study
Coefficient of determination
6. The probability of correctly detecting a false null hypothesis.
The Range
observational study
Power of a test
Statistic
7. A group of individuals sharing some common features that might affect the treatment.
Marginal probability
Correlation
Sample space
Block
8. 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).
Residuals
Simpson's Paradox
Kurtosis
Joint probability
9. The result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data
Posterior probability
Type 2 Error
An event
methods of least squares
10. When there is an even number of values...
Inferential
That is the median value
Probability density
Joint distribution
11. A measurement such that the random error is small
the population variance
Reliable measure
Type 2 Error
Probability and statistics
12. Gives the probability distribution for a continuous random variable.
A probability density function
That value is the median value
Null hypothesis
Simulation
13. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
Sampling
Variability
Law of Large Numbers
Type I errors & Type II errors
14. 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
Observational study
Pairwise independence
categorical variables
Probability and statistics
15. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
Prior probability
Particular realizations of a random variable
Marginal probability
Seasonal effect
16. Is the probability distribution - under repeated sampling of the population - of a given statistic.
Sampling
A sampling distribution
Posterior probability
Probability and statistics
17. Is its expected value. The mean (or sample mean of a data set is just the average value.
Probability and statistics
Mutual independence
The Mean of a random variable
Statistical dispersion
18. A numerical facsimilie or representation of a real-world phenomenon.
Simulation
Dependent Selection
Kurtosis
Null hypothesis
19. A numerical measure that describes an aspect of a population.
Parameter
Type II errors
Ordinal measurements
A random variable
20. Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically - sometimes they are grouped together as
Lurking variable
the population variance
categorical variables
Variability
21. Have meaningful distances between measurements defined - but the zero value is arbitrary (as in the case with longitude and temperature measurements in Celsius or Fahrenheit)
Interval measurements
That is the median value
Probability density
the population mean
22. Is a sample and the associated data points.
A data set
A data point
observational study
Valid measure
23. A consistent - repeated deviation of the sample statistic from the population parameter in the same direction when many samples are taken.
Variable
Bias
Probability density
An experimental study
24. 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
Probability
A probability density function
The Covariance between two random variables X and Y - with expected values E(X) =
Step 2 of a statistical experiment
25. Is the result of applying a statistical algorithm to a data set. It can also be described as an observable random variable.
A statistic
Nominal measurements
Reliable measure
A probability density function
26. Descriptive statistics and inferential statistics (a.k.a. - predictive statistics) together comprise
applied statistics
Type 1 Error
Residuals
Sampling Distribution
27. Some commonly used symbols for sample statistics
A statistic
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Posterior probability
A Statistical parameter
28. 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.
Step 2 of a statistical experiment
Simple random sample
Type 1 Error
Independent Selection
29. (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.
P-value
nominal - ordinal - interval - and ratio
An Elementary event
Probability
30. 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.
Law of Large Numbers
Statistical inference
Conditional distribution
The variance of a random variable
31. Used to reduce bias - this measure weights the more relevant information higher than less relevant info.
Valid measure
Ratio measurements
Likert scale
Statistical adjustment
32. To prove the guiding theory further - these predictions are tested as well - as part of the scientific method. If the inference holds true - then the descriptive statistics of the new data increase the soundness of that
categorical variables
hypothesis
A data point
Divide the sum by the number of values.
33. Is denoted by - pronounced 'x bar'.
Simpson's Paradox
expected value of X
Average and arithmetic mean
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
34. Is a subset of the sample space - to which a probability can be assigned. For example - on rolling a die - 'getting a five or a six' is an event (with a probability of one third if the die is fair).
An event
Type II errors
A likelihood function
the sample or population mean
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.
Correlation
Sampling Distribution
Probability density
Kurtosis
36. 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.
covariance of X and Y
Independent Selection
Estimator
The Mean of a random variable
37. Is the probability of some event A - assuming event B. Conditional probability is written P(A|B) - and is read 'the probability of A - given B'
f(z) - and its cdf by F(z).
The sample space
Conditional probability
Cumulative distribution functions
38. 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
Skewness
Type I errors & Type II errors
A probability space
Average and arithmetic mean
39. Is data arising from counting that can take only non-negative integer values.
The sample space
Count data
Standard error
The Range
40. E[X] :
s-algebras
the sample or population mean
Bias
expected value of X
41. 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.
An experimental study
A Distribution function
Variability
Estimator
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. A numerical measure that assesses the strength of a linear relationship between two variables.
Correlation coefficient
inferential statistics
Particular realizations of a random variable
Null hypothesis
44. Some commonly used symbols for population parameters
Likert scale
Type I errors
That is the median value
the population mean
45. (or multivariate random variable) is a vector whose components are random variables on the same probability space.
The Range
Alpha value (Level of Significance)
A Random vector
Block
46. 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.
Divide the sum by the number of values.
Descriptive
covariance of X and Y
Marginal distribution
47. The collection of all possible outcomes in an experiment.
Step 3 of a statistical experiment
Sample space
Sampling
Divide the sum by the number of values.
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
A data point
Kurtosis
Random variables
49. A variable describes an individual by placing the individual into a category or a group.
inferential statistics
Probability
Qualitative variable
f(z) - and its cdf by F(z).
50. 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 probability density function
P-value
Mutual independence
The median value
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