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Test your basic knowledge |
CLEP General Mathematics: Probability And Statistics
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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 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 Mean of a random variable
A population or statistical population
Treatment
A probability density function
2. Descriptive statistics and inferential statistics (a.k.a. - predictive statistics) together comprise
The variance of a random variable
applied statistics
Parameter
A Statistical parameter
3. 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.
An Elementary event
An experimental study
A probability space
Individual
4. 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.
Likert scale
Greek letters
Marginal probability
Lurking variable
5. (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
the population mean
A likelihood function
Mutual independence
Type II errors
6. Is a function that gives the probability of all elements in a given space: see List of probability distributions
Statistics
Greek letters
A probability distribution
Observational study
7. Is a sample space over which a probability measure has been defined.
Correlation coefficient
A probability space
Atomic event
s-algebras
8. When you have two or more competing models - choose the simpler of the two models.
variance of X
Law of Parsimony
A probability distribution
A sample
9. 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
A likelihood function
Step 3 of a statistical experiment
the population cumulants
Statistics
10. 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
Descriptive
Power of a test
Ratio measurements
A probability density function
11. 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.
observational study
A probability density function
Seasonal effect
Type 2 Error
12. 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
Power of a test
Skewness
Binary data
Seasonal effect
13. 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
hypotheses
inferential statistics
A population or statistical population
14. 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
Probability density
Cumulative distribution functions
Lurking variable
Step 2 of a statistical experiment
15. Statistics involve methods of using information from a sample to draw conclusions regarding the population.
An event
Inferential
the population correlation
Interval measurements
16. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
Probability and statistics
Inferential
Binary data
Pairwise independence
17. When info. in a contingency table is re-organized into more or less categories - relationships seen can change or reverse.
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18. 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.
Ratio measurements
The Mean of a random variable
Kurtosis
Estimator
19. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
Skewness
Greek letters
Prior probability
Interval measurements
20. To find the average - or arithmetic mean - of a set of numbers:
Divide the sum by the number of values.
The Covariance between two random variables X and Y - with expected values E(X) =
Credence
Count data
21. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.
Prior probability
Greek letters
An estimate of a parameter
s-algebras
22. Cov[X - Y] :
covariance of X and Y
The average - or arithmetic mean
variance of X
the population variance
23. Working from a null hypothesis two basic forms of error are recognized:
Probability density functions
experimental studies and observational studies.
Greek letters
Type I errors & Type II errors
24. A subjective estimate of probability.
Coefficient of determination
Credence
Interval measurements
Correlation
25. Given two random variables X and Y - the joint distribution of X and Y is the probability distribution of X and Y together.
the sample or population mean
Joint distribution
Binary data
An estimate of a parameter
26. In particular - the pdf of the standard normal distribution is denoted by
Statistics
A data set
f(z) - and its cdf by F(z).
The variance of a random variable
27. Statistical methods can be used for summarizing or describing a collection of data; this is called
descriptive statistics
Sample space
categorical variables
Null hypothesis
28. The probability of correctly detecting a false null hypothesis.
The median value
Power of a test
Probability
the sample or population mean
29. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
The sample space
Statistical dispersion
Outlier
Law of Large Numbers
30. Is the result of applying a statistical algorithm to a data set. It can also be described as an observable random variable.
Parameter - or 'statistical parameter'
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Trend
A statistic
31. 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
Type I errors
Probability
Trend
An estimate of a parameter
32. 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
Statistics
Mutual independence
The median value
P-value
33. Two variables such that their effects on the response variable cannot be distinguished from each other.
Individual
Confounded variables
Joint probability
Trend
34. ?r
the population cumulants
Simple random sample
Beta value
The variance of a random variable
35. A data value that falls outside the overall pattern of the graph.
Outlier
variance of X
Quantitative variable
A sampling distribution
36. Describes the spread in the values of the sample statistic when many samples are taken.
Ratio measurements
Skewness
Variability
Type I errors
37. Is that part of a population which is actually observed.
A sample
Placebo effect
Experimental and observational studies
Estimator
38. The collection of all possible outcomes in an experiment.
observational study
Sample space
Likert scale
A statistic
39. 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
Bias
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
40. ?
methods of least squares
A data set
The standard deviation
the population correlation
41. The objects described by a set of data: person (animal) - place - and - thing. (SUBJECTS)
Statistics
Coefficient of determination
Individual
f(z) - and its cdf by F(z).
42. 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).
Simple random sample
Standard error
Correlation
Joint probability
43. Is the most commonly used measure of statistical dispersion. It is the square root of the variance - and is generally written s (sigma).
Block
Sampling frame
Particular realizations of a random variable
The standard deviation
44. Are usually written with upper case calligraphic (e.g. F for the set of sets on which we define the probability P)
s-algebras
Qualitative variable
Sample space
Conditional probability
45. Error also refers to the extent to which individual observations in a sample differ from a central value - such as
Power of a test
the sample or population mean
The sample space
inferential statistics
46. 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
Qualitative variable
Greek letters
Joint distribution
Descriptive statistics
47. A numerical measure that describes an aspect of a sample.
An estimate of a parameter
Statistic
Quantitative variable
Sampling frame
48. The proportion of the explained variation by a linear regression model in the total variation.
Type II errors
A probability space
Power of a test
Coefficient of determination
49. (or multivariate random variable) is a vector whose components are random variables on the same probability space.
Conditional probability
A Random vector
An Elementary event
descriptive statistics
50. Some commonly used symbols for population parameters
An event
the population mean
The Expected value
Correlation coefficient