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Test your basic knowledge |
CLEP General Mathematics: Probability And Statistics
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Subjects
:
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
.
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. A sample selected in such a way that each individual is equally likely to be selected as well as any group of size n is equally likely to be selected.
A sample
f(z) - and its cdf by F(z).
Confounded variables
Simple random sample
2. 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.
Ordinal measurements
An event
Bias
The median value
3. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
Beta value
Marginal probability
Seasonal effect
Pairwise independence
4. Working from a null hypothesis two basic forms of error are recognized:
Type I errors & Type II errors
Step 1 of a statistical experiment
categorical variables
Bias
5. Some commonly used symbols for sample statistics
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Marginal distribution
The Covariance between two random variables X and Y - with expected values E(X) =
Law of Large Numbers
6. ?r
the population cumulants
The Covariance between two random variables X and Y - with expected values E(X) =
Parameter - or 'statistical parameter'
Inferential
7. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.
Nominal measurements
Descriptive
Block
The Covariance between two random variables X and Y - with expected values E(X) =
8. 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.
The sample space
Conditional distribution
Reliable measure
A sample
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
Statistics
Qualitative variable
Power of a test
hypothesis
10. A variable has a value or numerical measurement for which operations such as addition or averaging make sense.
Quantitative variable
Estimator
A probability density function
Conditional distribution
11. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.
An estimate of a parameter
The Expected value
Divide the sum by the number of values.
Lurking variable
12. (also called statistical variability) is a measure of how diverse some data is. It can be expressed by the variance or the standard deviation.
That value is the median value
Interval measurements
Statistical dispersion
Trend
13. Is defined as the expected value of random variable (X -
An Elementary event
The Covariance between two random variables X and Y - with expected values E(X) =
quantitative variables
Independent Selection
14. Are usually written with upper case calligraphic (e.g. F for the set of sets on which we define the probability P)
The Range
inferential statistics
Variability
s-algebras
15. Have no meaningful rank order among values.
Variability
Conditional distribution
f(z) - and its cdf by F(z).
Nominal measurements
16. (e.g. ? - b) are commonly used to denote unknown parameters (population parameters).
Ratio measurements
P-value
Simpson's Paradox
Greek letters
17. Used to reduce bias - this measure weights the more relevant information higher than less relevant info.
Prior probability
Type II errors
Statistical adjustment
Observational study
18. 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
Marginal distribution
Mutual independence
descriptive statistics
Sampling
19. 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
The sample space
Bias
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Step 2 of a statistical experiment
20. 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
Credence
Type 2 Error
The Expected value
21. 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).
An estimate of a parameter
A Distribution function
Joint probability
the population correlation
22. 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
The Mean of a random variable
Simulation
Confounded variables
Skewness
23. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively
A population or statistical population
applied statistics
A statistic
Residuals
24. A scale that represents an ordinal scale such as looks on a scale from 1 to 10.
Residuals
Likert scale
Step 3 of a statistical experiment
Sampling Distribution
25. Describes a characteristic of an individual to be measured or observed.
Type 2 Error
Variable
Statistical adjustment
The median value
26. When you have two or more competing models - choose the simpler of the two models.
Conditional distribution
Law of Parsimony
Count data
descriptive statistics
27. (pdfs) and probability mass functions are denoted by lower case letters - e.g. f(x).
An experimental study
Probability density functions
Binary data
Probability and statistics
28. 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 experimental study
Bias
An event
Probability density
29. Occurs when a subject receives no treatment - but (incorrectly) believes he or she is in fact receiving treatment and responds favorably.
Type 2 Error
Bias
A sample
Placebo effect
30. Is its expected value. The mean (or sample mean of a data set is just the average value.
Type 1 Error
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Statistical dispersion
The Mean of a random variable
31. 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
Average and arithmetic mean
Power of a test
Null hypothesis
Qualitative variable
32. The proportion of the explained variation by a linear regression model in the total variation.
Coefficient of determination
methods of least squares
The sample space
Simulation
33. Where the null hypothesis fails to be rejected and an actual difference between populations is missed giving a 'false negative'.
Interval measurements
Step 1 of a statistical experiment
Prior probability
Type II errors
34. Failing to reject a false null hypothesis.
the population cumulants
Seasonal effect
Type 2 Error
Skewness
35. Of a group of numbers is the center point of all those number values.
The average - or arithmetic mean
Nominal measurements
Posterior probability
Atomic event
36. A subjective estimate of probability.
Statistical inference
The Mean of a random variable
Lurking variable
Credence
37. The probability of correctly detecting a false null hypothesis.
A sampling distribution
A Statistical parameter
A probability density function
Power of a test
38. A group of individuals sharing some common features that might affect the treatment.
That is the median value
Simpson's Paradox
Prior probability
Block
39. A consistent - repeated deviation of the sample statistic from the population parameter in the same direction when many samples are taken.
Count data
Statistic
Bias
An event
40. Is denoted by - pronounced 'x bar'.
Seasonal effect
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
A statistic
A Probability measure
41. The collection of all possible outcomes in an experiment.
Statistical adjustment
Sample space
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
the population mean
42. 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
A Distribution function
Treatment
hypothesis
43. A data value that falls outside the overall pattern of the graph.
quantitative variables
Conditional probability
The Expected value
Outlier
44. A numerical measure that describes an aspect of a population.
Parameter
A sample
Skewness
A random variable
45. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
Variability
the sample or population mean
hypothesis
nominal - ordinal - interval - and ratio
46. Probability of accepting a false null hypothesis.
Joint distribution
Standard error
Beta value
Marginal distribution
47. Have imprecise differences between consecutive values - but have a meaningful order to those values
A sampling distribution
The standard deviation
The Expected value
Ordinal measurements
48. 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.
Interval measurements
Statistical dispersion
Sample space
A data point
49. Long-term upward or downward movement over time.
An event
Individual
Trend
hypothesis
50. A measure that is relevant or appropriate as a representation of that property.
Valid measure
Sampling
observational study
Parameter - or 'statistical parameter'