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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. Are usually written in upper case roman letters: X - Y - etc.
Placebo effect
s-algebras
Random variables
Type II errors
2. 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)
Correlation
Interval measurements
A sampling distribution
Bias
3. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
applied statistics
Count data
Probability
nominal - ordinal - interval - and ratio
4. 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
A sample
Step 2 of a statistical experiment
quantitative variables
Binary data
5. 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 arithmetic mean of a set of numbers x1 - x2 - ... - xn
Variable
Law of Parsimony
6. Is denoted by - pronounced 'x bar'.
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Treatment
Likert scale
The variance of a random variable
7. A measure that is relevant or appropriate as a representation of that property.
Average and arithmetic mean
Valid measure
the population cumulants
expected value of X
8. A variable that has an important effect on the response variable and the relationship among the variables in a study but is not one of the explanatory variables studied either because it is unknown or not measured.
Lurking variable
A likelihood function
Binary data
Estimator
9. Some commonly used symbols for population parameters
Average and arithmetic mean
A probability density function
Greek letters
the population mean
10. S^2
the population variance
Sampling frame
quantitative variables
That value is the median value
11. 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.
Probability
the population mean
The Mean of a random variable
That value is the median value
12. 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.
A Distribution function
Cumulative distribution functions
Type II errors
Correlation coefficient
13. Gives the probability of events in a probability space.
Simpson's Paradox
A Probability measure
Dependent Selection
Joint distribution
14. A collection of events is mutually independent if for any subset of the collection - the joint probability of all events occurring is equal to the product of the joint probabilities of the individual events. Think of the result of a series of coin-fl
Mutual independence
Descriptive
Conditional probability
Ordinal measurements
15. 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}.
Prior probability
Qualitative variable
variance of X
The sample space
16. Patterns in the data may be modeled in a way that accounts for randomness and uncertainty in the observations - and are then used for drawing inferences about the process or population being studied; this is called
Parameter - or 'statistical parameter'
Nominal measurements
inferential statistics
Probability and statistics
17. 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.
Type II errors
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
A likelihood function
Statistical inference
18. Ratio and interval measurements which can be either discrete or continuous - due to their numerical nature are grouped together as
observational study
quantitative variables
Statistical inference
the population mean
19. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.
The Expected value
Descriptive
Dependent Selection
The Range
20. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
A probability distribution
Sampling
An experimental study
Pairwise independence
21. Is a sample and the associated data points.
Prior probability
experimental studies and observational studies.
Step 2 of a statistical experiment
A data set
22. A consistent - repeated deviation of the sample statistic from the population parameter in the same direction when many samples are taken.
the population mean
Posterior probability
Bias
Placebo effect
23. 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.
Trend
A probability distribution
the population mean
A population or statistical population
24. Is a function that gives the probability of all elements in a given space: see List of probability distributions
Skewness
Divide the sum by the number of values.
A probability distribution
An Elementary event
25. Have imprecise differences between consecutive values - but have a meaningful order to those values
Statistical adjustment
Ordinal measurements
Greek letters
Conditional distribution
26. When you have two or more competing models - choose the simpler of the two models.
expected value of X
Law of Parsimony
Type I errors
Pairwise independence
27. Is the most commonly used measure of statistical dispersion. It is the square root of the variance - and is generally written s (sigma).
Skewness
A sample
The standard deviation
Law of Large Numbers
28. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.
An estimate of a parameter
Seasonal effect
Statistical inference
Prior probability
29. 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
Seasonal effect
expected value of X
Skewness
Random variables
30. 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
the sample or population mean
Cumulative distribution functions
Descriptive statistics
the population mean
31. 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 and statistics
A Random vector
A random variable
f(z) - and its cdf by F(z).
32. Is the length of the smallest interval which contains all the data.
The Range
Treatment
A Random vector
The variance of a random variable
33. E[X] :
Outlier
f(z) - and its cdf by F(z).
Sample space
expected value of X
34.
the population mean
observational study
That is the median value
Power of a test
35. Is the probability distribution - under repeated sampling of the population - of a given statistic.
The Mean of a random variable
Probability and statistics
Observational study
A sampling distribution
36. 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.
the sample or population mean
P-value
Bias
Marginal probability
37. A list of individuals from which the sample is actually selected.
Sampling frame
Divide the sum by the number of values.
Random variables
The sample space
38. Are usually written with upper case calligraphic (e.g. F for the set of sets on which we define the probability P)
A Random vector
Residuals
Sample space
s-algebras
39. Some commonly used symbols for sample statistics
observational study
Posterior probability
A probability distribution
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
40. Probability of accepting a false null hypothesis.
Type I errors
Treatment
variance of X
Beta value
41. (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.
descriptive statistics
Estimator
Simple random sample
An Elementary event
42. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
Seasonal effect
Posterior probability
Sampling Distribution
the sample or population mean
43. Is the result of applying a statistical algorithm to a data set. It can also be described as an observable random variable.
Descriptive
A statistic
Simpson's Paradox
Binomial experiment
44. 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.
Statistics
Statistic
The median value
Trend
45. When there is an even number of values...
That is the median value
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Random variables
the sample or population mean
46. A variable describes an individual by placing the individual into a category or a group.
Qualitative variable
Experimental and observational studies
Step 1 of a statistical experiment
Descriptive
47. (or multivariate random variable) is a vector whose components are random variables on the same probability space.
A data set
Bias
A likelihood function
A Random vector
48. 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 population cumulants
Individual
The variance of a random variable
Average and arithmetic mean
49. 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.
A Distribution function
Credence
Estimator
Placebo effect
50. 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
An event
The average - or arithmetic mean
Trend
Step 3 of a statistical experiment