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Test your basic knowledge |
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.
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. 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
The variance of a random variable
Independent Selection
A statistic
2. When info. in a contingency table is re-organized into more or less categories - relationships seen can change or reverse.
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3. A subjective estimate of probability.
Credence
An event
Lurking variable
Seasonal effect
4. The collection of all possible outcomes in an experiment.
Sample space
Random variables
Seasonal effect
expected value of X
5. Many statistical methods seek to minimize the mean-squared error - and these are called
Random variables
Estimator
methods of least squares
A statistic
6. Working from a null hypothesis two basic forms of error are recognized:
Average and arithmetic mean
Pairwise independence
Type I errors & Type II errors
Beta value
7. 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
An experimental study
Prior probability
Statistic
8. When you have two or more competing models - choose the simpler of the two models.
A Statistical parameter
A data point
Seasonal effect
Law of Parsimony
9. 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
Descriptive statistics
hypothesis
The average - or arithmetic mean
Sampling Distribution
10. 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
Step 3 of a statistical experiment
Correlation
Correlation coefficient
A sample
11. Cov[X - Y] :
Power of a test
covariance of X and Y
Ordinal measurements
Prior probability
12. Have no meaningful rank order among values.
Sampling Distribution
A probability distribution
Nominal measurements
The Mean of a random variable
13. 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
descriptive statistics
Qualitative variable
A data point
Inferential statistics
14. A data value that falls outside the overall pattern of the graph.
Residuals
Outlier
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Reliable measure
15. Gives the probability distribution for a continuous random variable.
the population mean
A probability density function
covariance of X and Y
Atomic event
16. Have both a meaningful zero value and the distances between different measurements defined; they provide the greatest flexibility in statistical methods that can be used for analyzing the data
Mutual independence
Skewness
Ratio measurements
Law of Large Numbers
17. 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).
Binary data
Type I errors
An event
Likert scale
18. 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
Nominal measurements
Experimental and observational studies
Probability
Confounded variables
19. Is denoted by - pronounced 'x bar'.
Mutual independence
Simulation
Quantitative variable
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
20. Given two random variables X and Y - the joint distribution of X and Y is the probability distribution of X and Y together.
descriptive statistics
experimental studies and observational studies.
Joint distribution
Simple random sample
21. A numerical facsimilie or representation of a real-world phenomenon.
Type 1 Error
Descriptive statistics
Simulation
Bias
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
Treatment
the population cumulants
Descriptive statistics
covariance of X and Y
23. A consistent - repeated deviation of the sample statistic from the population parameter in the same direction when many samples are taken.
Joint distribution
A Statistical parameter
Bias
Ratio measurements
24. 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 Statistical parameter
Sampling frame
The median value
the population cumulants
25. Probability of rejecting a true null hypothesis.
The average - or arithmetic mean
Skewness
P-value
Alpha value (Level of Significance)
26. The proportion of the explained variation by a linear regression model in the total variation.
Descriptive statistics
Coefficient of determination
Marginal probability
Credence
27. Another name for elementary event.
observational study
Probability density
Atomic event
A random variable
28. 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
Confounded variables
Type II errors
An event
29. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
Confounded variables
Type II errors
Divide the sum by the number of values.
Pairwise independence
30. (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.
An Elementary event
Coefficient of determination
Parameter - or 'statistical parameter'
Cumulative distribution functions
31.
the population mean
covariance of X and Y
the population correlation
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
32. 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.
Variable
Step 2 of a statistical experiment
variance of X
A Distribution function
33. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
The average - or arithmetic mean
Sampling Distribution
Residuals
A sample
34. (or expectation) of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by its payoff ('value'). Thus - it represents the average amount one 'expects' to win per bet if bets with identical odds are re
The Mean of a random variable
A Random vector
The Expected value
Statistic
35. There are two major types of causal statistical studies: In both types of studies - the effect of differences of an independent variable (or variables) on the behavior of the dependent variable are observed. The difference between the two types lies
experimental studies and observational studies.
Statistical dispersion
Atomic event
quantitative variables
36. Is the probability distribution - under repeated sampling of the population - of a given statistic.
Binomial experiment
Atomic event
A sampling distribution
Law of Large Numbers
37. 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
Qualitative variable
P-value
Divide the sum by the number of values.
hypotheses
38. 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
A Statistical parameter
Posterior probability
Type I errors
39. 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.
That value is the median value
Step 3 of a statistical experiment
Type 2 Error
Dependent Selection
40. Are simply two different terms for the same thing. Add the given values
Average and arithmetic mean
Treatment
Binomial experiment
A data set
41. Involves taking measurements of the system under study - manipulating the system - and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements.
The standard deviation
The sample space
An experimental study
Inferential statistics
42. S^2
Seasonal effect
the population variance
Likert scale
Bias
43. 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.
Interval measurements
A population or statistical population
Probability and statistics
Type 1 Error
44. Describes a characteristic of an individual to be measured or observed.
Pairwise independence
Count data
Particular realizations of a random variable
Variable
45. 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
Beta value
Probability density
The standard deviation
methods of least squares
46. A common goal for a statistical research project is to investigate causality - and in particular to draw a conclusion on the effect of changes in the values of predictors or independent variables on dependent variables or response.
Experimental and observational studies
The standard deviation
Simulation
A Statistical parameter
47. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
P-value
Count data
Sampling frame
quantitative variables
48. (or multivariate random variable) is a vector whose components are random variables on the same probability space.
A Random vector
The Expected value
Independent Selection
A probability space
49. 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.
A Random vector
Statistics
Probability density functions
A data point
50. Is the probability of an event - ignoring any information about other events. The marginal probability of A is written P(A). Contrast with conditional probability.
Joint probability
Power of a test
Marginal probability
A statistic