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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. (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
Step 1 of a statistical experiment
The Expected value
An experimental study
Type I errors & Type II errors
2. ?r
Pairwise independence
the population cumulants
Greek letters
Parameter
3. Is a parameter that indexes a family of probability distributions.
A Statistical parameter
Skewness
Outlier
Conditional probability
4. A numerical measure that describes an aspect of a sample.
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Statistic
Quantitative variable
Experimental and observational studies
5. Is the length of the smallest interval which contains all the data.
Simple random sample
Valid measure
The Range
Parameter
6. Probability of accepting a false null hypothesis.
Bias
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Ordinal measurements
Beta value
7. 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}.
Probability density functions
The sample space
Sampling
Conditional probability
8. 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
Independent Selection
Experimental and observational studies
quantitative variables
9. Ratio and interval measurements which can be either discrete or continuous - due to their numerical nature are grouped together as
An experimental study
Inferential
quantitative variables
A data set
10. Gives the probability of events in a probability space.
A Probability measure
Random variables
Joint distribution
Skewness
11. 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
Statistical adjustment
That value is the median value
Atomic event
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
variance of X
Trend
A Probability measure
Skewness
13. A variable describes an individual by placing the individual into a category or a group.
Independent Selection
Law of Large Numbers
Qualitative variable
A Probability measure
14. Is data arising from counting that can take only non-negative integer values.
Quantitative variable
Count data
Lurking variable
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
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.
Statistics
Quantitative variable
Coefficient of determination
The Covariance between two random variables X and Y - with expected values E(X) =
16. Long-term upward or downward movement over time.
Observational study
A sample
Trend
Inferential
17. Is the most commonly used measure of statistical dispersion. It is the square root of the variance - and is generally written s (sigma).
hypotheses
Joint probability
An experimental study
The standard deviation
18. A measure that is relevant or appropriate as a representation of that property.
Independence or Statistical independence
expected value of X
Experimental and observational studies
Valid measure
19. 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
A probability distribution
Independence or Statistical independence
Divide the sum by the number of values.
Block
20. 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)
Probability
Quantitative variable
Inferential statistics
Interval measurements
21. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.
Descriptive
Estimator
P-value
Inferential statistics
22. To find the average - or arithmetic mean - of a set of numbers:
Divide the sum by the number of values.
Type I errors
The Range
Law of Large Numbers
23. (also called statistical variability) is a measure of how diverse some data is. It can be expressed by the variance or the standard deviation.
Statistical inference
Seasonal effect
Statistical dispersion
Type II errors
24. 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.
A likelihood function
That value is the median value
That is the median value
A probability density function
25. Var[X] :
variance of X
Observational study
A data point
Simulation
26. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively
Ratio measurements
Residuals
observational study
s-algebras
27. Error also refers to the extent to which individual observations in a sample differ from a central value - such as
Joint probability
the sample or population mean
That value is the median value
Type 2 Error
28. 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.
Joint distribution
A random variable
Simple random sample
Ordinal measurements
29. Of a group of numbers is the center point of all those number values.
the population variance
Independent Selection
Greek letters
The average - or arithmetic mean
30. Is a measure of the 'peakedness' of the probability distribution of a real-valued random variable. Higher kurtosis means more of the variance is due to infrequent extreme deviations - as opposed to frequent modestly sized deviations.
categorical variables
Kurtosis
descriptive statistics
Simpson's Paradox
31. Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically - sometimes they are grouped together as
covariance of X and Y
Residuals
categorical variables
A sample
32. Working from a null hypothesis two basic forms of error are recognized:
Type I errors & Type II errors
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Credence
Likert scale
33. Are written in corresponding lower case letters. For example x1 - x2 - ... - xn could be a sample corresponding to the random variable X.
Probability and statistics
observational study
Particular realizations of a random variable
variance of X
34. When there is an even number of values...
Skewness
That is the median value
Statistical adjustment
Probability
35. Where the null hypothesis fails to be rejected and an actual difference between populations is missed giving a 'false negative'.
Observational study
Skewness
Type II errors
Binary data
36. A scale that represents an ordinal scale such as looks on a scale from 1 to 10.
the population mean
Conditional distribution
Likert scale
That value is the median value
37. Can be a population parameter - a distribution parameter - an unobserved parameter (with different shades of meaning). In statistics - this is often a quantity to be estimated.
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38. A consistent - repeated deviation of the sample statistic from the population parameter in the same direction when many samples are taken.
The standard deviation
The Range
An Elementary event
Bias
39. (pdfs) and probability mass functions are denoted by lower case letters - e.g. f(x).
quantitative variables
Probability density functions
Individual
Pairwise independence
40. The proportion of the explained variation by a linear regression model in the total variation.
Simpson's Paradox
An Elementary event
Coefficient of determination
A Statistical parameter
41. When info. in a contingency table is re-organized into more or less categories - relationships seen can change or reverse.
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42. ?
the population correlation
the sample or population mean
Conditional distribution
Confounded variables
43. Many statistical methods seek to minimize the mean-squared error - and these are called
A data set
Simple random sample
An experimental study
methods of least squares
44. Statistics involve methods of using information from a sample to draw conclusions regarding the population.
Inferential
A statistic
Binomial experiment
An event
45. 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
observational study
the population cumulants
Coefficient of determination
inferential statistics
46. Is a function that gives the probability of all elements in a given space: see List of probability distributions
methods of least squares
Block
A probability distribution
Lurking variable
47. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
Step 2 of a statistical experiment
Null hypothesis
Count data
Pairwise independence
48. 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.
Descriptive
hypotheses
An experimental study
Divide the sum by the number of values.
49. The collection of all possible outcomes in an experiment.
Trend
The average - or arithmetic mean
Residuals
Sample space
50. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
A population or statistical population
Conditional probability
A probability space
Prior probability