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Test your basic knowledge |
CLEP General Mathematics: Probability And Statistics
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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. Error also refers to the extent to which individual observations in a sample differ from a central value - such as
Type I errors & Type II errors
Mutual independence
Descriptive
the sample or population mean
2. Is its expected value. The mean (or sample mean of a data set is just the average value.
A probability distribution
inferential statistics
A statistic
The Mean of a random variable
3. 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.
inferential statistics
A random variable
Random variables
Experimental and observational studies
4. Is denoted by - pronounced 'x bar'.
methods of least squares
P-value
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Type I errors
5. Is that part of a population which is actually observed.
A Random vector
A sample
Inferential
methods of least squares
6. Is data that can take only two values - usually represented by 0 and 1.
Greek letters
Kurtosis
Beta value
Binary data
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
hypotheses
Simple random sample
Independence or Statistical independence
Sampling Distribution
8. 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.
Marginal probability
Simulation
Bias
the population cumulants
9. A group of individuals sharing some common features that might affect the treatment.
A sampling distribution
Block
Treatment
Lurking variable
10. A measure that is relevant or appropriate as a representation of that property.
Type 2 Error
A random variable
Valid measure
Bias
11. 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
Independence or Statistical independence
nominal - ordinal - interval - and ratio
Parameter
hypotheses
12. 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.
Mutual independence
A data point
Pairwise independence
Step 2 of a statistical experiment
13. 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}.
The sample space
An experimental study
Nominal measurements
A probability density function
14. 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
Bias
Probability
A Statistical parameter
Simulation
15. Is the study of the collection - organization - analysis - and interpretation of data. It deals with all aspects of this - including the planning of data collection in terms of the design of surveys and experiments.
Divide the sum by the number of values.
Lurking variable
observational study
Statistics
16. Long-term upward or downward movement over time.
the population correlation
hypothesis
Trend
Sampling frame
17. Given two random variables X and Y - the joint distribution of X and Y is the probability distribution of X and Y together.
s-algebras
Joint distribution
Cumulative distribution functions
observational study
18. 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.
The Covariance between two random variables X and Y - with expected values E(X) =
A sampling distribution
Dependent Selection
Valid measure
19. Two variables such that their effects on the response variable cannot be distinguished from each other.
Law of Large Numbers
Probability density functions
Divide the sum by the number of values.
Confounded variables
20. 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
Type 2 Error
quantitative variables
Marginal distribution
21. Var[X] :
covariance of X and Y
variance of X
A Random vector
Descriptive statistics
22. When you have two or more competing models - choose the simpler of the two models.
That value is the median value
Atomic event
quantitative variables
Law of Parsimony
23. The objects described by a set of data: person (animal) - place - and - thing. (SUBJECTS)
variance of X
Individual
Interval measurements
Block
24. The result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data
Variability
Ordinal measurements
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Posterior probability
25. Probability of accepting a false null hypothesis.
expected value of X
Likert scale
Beta value
Joint distribution
26. A numerical measure that describes an aspect of a sample.
Sample space
A Distribution function
Joint distribution
Statistic
27. Describes the spread in the values of the sample statistic when many samples are taken.
P-value
The Mean of a random variable
Placebo effect
Variability
28. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.
Independent Selection
An estimate of a parameter
A data point
observational study
29. Is a sample and the associated data points.
A random variable
Likert scale
Variability
A data set
30. 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.
Dependent Selection
A probability distribution
Estimator
The variance of a random variable
31. 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.
expected value of X
Statistical inference
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Likert scale
32. 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.
Likert scale
Beta value
Simple random sample
Sampling
33. ?
expected value of X
the population correlation
Descriptive statistics
Simulation
34. (e.g. ? - b) are commonly used to denote unknown parameters (population parameters).
Lurking variable
Greek letters
That is the median value
Type 2 Error
35. (pdfs) and probability mass functions are denoted by lower case letters - e.g. f(x).
Confounded variables
descriptive statistics
Simulation
Probability density functions
36. Of a group of numbers is the center point of all those number values.
Treatment
The average - or arithmetic mean
Statistical dispersion
Dependent Selection
37. Some commonly used symbols for sample statistics
A probability space
nominal - ordinal - interval - and ratio
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Lurking variable
38. 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
Random variables
Null hypothesis
A probability distribution
Simulation
39. Consists of a number of independent trials repeated under identical conditions. On each trial - there are two possible outcomes.
Quantitative variable
quantitative variables
Binomial experiment
covariance of X and Y
40. Any specific experimental condition applied to the subjects
Posterior probability
Treatment
observational study
Step 3 of a statistical experiment
41. Is one that explores the correlation between smoking and lung cancer. This type of study typically uses a survey to collect observations about the area of interest and then performs statistical analysis. In this case - the researchers would collect o
Skewness
A statistic
quantitative variables
Observational study
42. Is data arising from counting that can take only non-negative integer values.
Statistic
Statistical inference
Count data
Observational study
43. A subjective estimate of probability.
Sampling frame
Cumulative distribution functions
Beta value
Credence
44. (or multivariate random variable) is a vector whose components are random variables on the same probability space.
Qualitative variable
Descriptive statistics
Marginal distribution
A Random vector
45. The collection of all possible outcomes in an experiment.
Sample space
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
The Expected value
hypotheses
46. 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.
Coefficient of determination
Bias
A Distribution function
Power of a test
47. Are written in corresponding lower case letters. For example x1 - x2 - ... - xn could be a sample corresponding to the random variable X.
A probability distribution
Seasonal effect
Correlation
Particular realizations of a random variable
48. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
A probability distribution
A data set
Parameter
Pairwise independence
49. 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.
Step 1 of a statistical experiment
Binomial experiment
Conditional distribution
Reliable measure
50. Cov[X - Y] :
Experimental and observational studies
The Range
Valid measure
covariance of X and Y