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Test your basic knowledge |
CLEP General Mathematics: Probability And Statistics
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Subjects
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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. Can refer either to a sample not being representative of the population - or to the difference between the expected value of an estimator and the true value.
Bias
Variability
Particular realizations of a random variable
Simple random sample
2. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.
A likelihood function
Descriptive
Skewness
A sampling distribution
3. 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.
hypothesis
A data point
hypotheses
Variability
4. 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.
The variance of a random variable
the sample or population mean
A population or statistical population
Sampling
5. 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).
Joint probability
Count data
Credence
categorical variables
6. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively
A Statistical parameter
A probability space
Residuals
the population cumulants
7. 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 arithmetic mean of a set of numbers x1 - x2 - ... - xn
Independence or Statistical independence
An estimate of a parameter
Alpha value (Level of Significance)
8. 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.
Individual
A probability distribution
experimental studies and observational studies.
Sampling
9. Are written in corresponding lower case letters. For example x1 - x2 - ... - xn could be a sample corresponding to the random variable X.
hypotheses
The Expected value
Particular realizations of a random variable
the population variance
10. A measurement such that the random error is small
Reliable measure
A random variable
Sampling Distribution
nominal - ordinal - interval - and ratio
11. (or multivariate random variable) is a vector whose components are random variables on the same probability space.
Estimator
the population variance
Statistics
A Random vector
12. When info. in a contingency table is re-organized into more or less categories - relationships seen can change or reverse.
13. A subjective estimate of probability.
A Random vector
Statistical dispersion
Inferential
Credence
14. Some commonly used symbols for population parameters
Inferential statistics
Interval measurements
inferential statistics
the population mean
15. Two variables such that their effects on the response variable cannot be distinguished from each other.
Confounded variables
Mutual independence
A probability density function
Estimator
16. Where the null hypothesis fails to be rejected and an actual difference between populations is missed giving a 'false negative'.
Type II errors
Placebo effect
Type 2 Error
the population correlation
17. Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically - sometimes they are grouped together as
Valid measure
Step 3 of a statistical experiment
categorical variables
Power of a test
18. Failing to reject a false null hypothesis.
Type 2 Error
A random variable
The Range
Conditional probability
19. Is the probability distribution - under repeated sampling of the population - of a given statistic.
A probability space
nominal - ordinal - interval - and ratio
A sampling distribution
The sample space
20. 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.
Variable
Outlier
That value is the median value
variance of X
21. Var[X] :
A Probability measure
variance of X
Statistical adjustment
Block
22. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
Statistical adjustment
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
P-value
hypotheses
23. A group of individuals sharing some common features that might affect the treatment.
Sampling Distribution
s-algebras
Block
the sample or population mean
24. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
Prior probability
P-value
observational study
Probability density functions
25. Is denoted by - pronounced 'x bar'.
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Ordinal measurements
Alpha value (Level of Significance)
Conditional distribution
26. A variable describes an individual by placing the individual into a category or a group.
A data point
Marginal probability
Qualitative variable
Block
27. E[X] :
That value is the median value
A Probability measure
expected value of X
Average and arithmetic mean
28. (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.
the population mean
An Elementary event
A sampling distribution
Parameter - or 'statistical parameter'
29. 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.
A Distribution function
A Random vector
nominal - ordinal - interval - and ratio
Kurtosis
30. 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
That is the median value
Step 3 of a statistical experiment
Simulation
Marginal probability
31. Cov[X - Y] :
Reliable measure
Step 3 of a statistical experiment
covariance of X and Y
Placebo effect
32. Have imprecise differences between consecutive values - but have a meaningful order to those values
Ordinal measurements
Inferential statistics
Probability density
nominal - ordinal - interval - and ratio
33. Is its expected value. The mean (or sample mean of a data set is just the average value.
Probability
Correlation
Parameter
The Mean of a random variable
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
Law of Parsimony
A likelihood function
Statistic
A Distribution function
35. Long-term upward or downward movement over time.
Trend
Estimator
Statistics
Placebo effect
36. 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'
Independence or Statistical independence
An estimate of a parameter
Confounded variables
Conditional probability
37. 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.
Probability density
A random variable
hypothesis
Mutual independence
38. 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.
Correlation coefficient
Average and arithmetic mean
Estimator
hypothesis
39. Descriptive statistics and inferential statistics (a.k.a. - predictive statistics) together comprise
the population mean
A Distribution function
Qualitative variable
applied statistics
40. A measure that is relevant or appropriate as a representation of that property.
Interval measurements
Inferential statistics
Valid measure
Qualitative variable
41. When you have two or more competing models - choose the simpler of the two models.
Law of Parsimony
Standard error
Sampling Distribution
Pairwise independence
42. (cdfs) are denoted by upper case letters - e.g. F(x).
Correlation coefficient
Cumulative distribution functions
Type II errors
Parameter - or 'statistical parameter'
43. 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)
Law of Large Numbers
categorical variables
Observational study
Interval measurements
44. 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
The standard deviation
The average - or arithmetic mean
Type I errors & Type II errors
45. A numerical facsimilie or representation of a real-world phenomenon.
Quantitative variable
Simulation
Atomic event
Block
46. A consistent - repeated deviation of the sample statistic from the population parameter in the same direction when many samples are taken.
experimental studies and observational studies.
Bias
A sample
Pairwise independence
47. Working from a null hypothesis two basic forms of error are recognized:
Type I errors & Type II errors
Pairwise independence
Trend
Power of a test
48. (pdfs) and probability mass functions are denoted by lower case letters - e.g. f(x).
Trend
Quantitative variable
Probability density functions
Qualitative variable
49. 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}.
An experimental study
Type II errors
methods of least squares
The sample space
50. Is defined as the expected value of random variable (X -
Sample space
The Covariance between two random variables X and Y - with expected values E(X) =
Statistical adjustment
Statistical dispersion