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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. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
Random variables
Descriptive statistics
Kurtosis
Pairwise independence
2. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
observational study
P-value
Marginal distribution
variance of X
3. Given two jointly distributed random variables X and Y - the marginal distribution of X is simply the probability distribution of X ignoring information about Y.
Qualitative variable
Particular realizations of a random variable
Binary data
Marginal distribution
4. 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.
Estimator
Bias
Ordinal measurements
Type 2 Error
5. A list of individuals from which the sample is actually selected.
Sampling frame
hypothesis
Pairwise independence
An estimate of a parameter
6. 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
Interval measurements
Dependent Selection
Independent Selection
7. (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
Average and arithmetic mean
Mutual independence
A likelihood function
The average - or arithmetic mean
8. 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.
quantitative variables
Step 2 of a statistical experiment
A random variable
The Covariance between two random variables X and Y - with expected values E(X) =
9. 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
Skewness
Alpha value (Level of Significance)
Particular realizations of a random variable
Conditional distribution
10. Probability of rejecting a true null hypothesis.
categorical variables
the sample or population mean
Sample space
Alpha value (Level of Significance)
11. ?r
Joint distribution
Residuals
Reliable measure
the population cumulants
12. A variable that has an important effect on the response variable and the relationship among the variables in a study but is not one of the explanatory variables studied either because it is unknown or not measured.
Estimator
Lurking variable
Sampling Distribution
A population or statistical population
13. Is data arising from counting that can take only non-negative integer values.
A probability distribution
Greek letters
Count data
Sampling
14. Ratio and interval measurements which can be either discrete or continuous - due to their numerical nature are grouped together as
Descriptive statistics
quantitative variables
Cumulative distribution functions
expected value of X
15. (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.
Experimental and observational studies
An Elementary event
Joint probability
Probability density
16. When info. in a contingency table is re-organized into more or less categories - relationships seen can change or reverse.
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17. Have no meaningful rank order among values.
The Range
Nominal measurements
Correlation coefficient
Ordinal measurements
18. To find the average - or arithmetic mean - of a set of numbers:
The median value
Probability density functions
P-value
Divide the sum by the number of values.
19. Of a group of numbers is the center point of all those number values.
The average - or arithmetic mean
Statistical dispersion
Experimental and observational studies
A likelihood function
20. Is that part of a population which is actually observed.
A sample
Bias
Ordinal measurements
Binary data
21. (or multivariate random variable) is a vector whose components are random variables on the same probability space.
A population or statistical population
Statistics
Simulation
A Random vector
22. Consists of a number of independent trials repeated under identical conditions. On each trial - there are two possible outcomes.
Simple random sample
Marginal probability
Binomial experiment
Marginal distribution
23. Is a sample and the associated data points.
Valid measure
A data set
Interval measurements
Pairwise independence
24. 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
A likelihood function
f(z) - and its cdf by F(z).
inferential statistics
25. S^2
covariance of X and Y
Particular realizations of a random variable
An Elementary event
the population variance
26. 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.
the population variance
Bias
Sampling
The median value
27. 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.
Statistical dispersion
A population or statistical population
Statistics
A sampling distribution
28.
the population mean
Statistical dispersion
s-algebras
Individual
29. A numerical measure that assesses the strength of a linear relationship between two variables.
s-algebras
Treatment
Correlation coefficient
An event
30. A data value that falls outside the overall pattern of the graph.
The average - or arithmetic mean
Outlier
The standard deviation
Variability
31. Var[X] :
Reliable measure
Outlier
descriptive statistics
variance of X
32. 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}.
Sample space
The sample space
The Expected value
Outlier
33. The result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data
Quantitative variable
The standard deviation
Posterior probability
Type 1 Error
34. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
Simpson's Paradox
Law of Large Numbers
The sample space
the population correlation
35. Data are gathered and correlations between predictors and response are investigated.
observational study
Conditional probability
Descriptive
experimental studies and observational studies.
36. Gives the probability distribution for a continuous random variable.
The average - or arithmetic mean
The Expected value
Credence
A probability density function
37. Are usually written with upper case calligraphic (e.g. F for the set of sets on which we define the probability P)
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
The Mean of a random variable
Bias
s-algebras
38. 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.
Bias
Seasonal effect
quantitative variables
Law of Large Numbers
39. A group of individuals sharing some common features that might affect the treatment.
Block
Divide the sum by the number of values.
Type 2 Error
The standard deviation
40. 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
Probability
Confounded variables
Nominal measurements
Prior probability
41. The collection of all possible outcomes in an experiment.
Sample space
descriptive statistics
Step 3 of a statistical experiment
A Probability measure
42. Is a measure of its statistical dispersion - indicating how far from the expected value its values typically are. The variance of random variable X is typically designated as - - or simply s2.
Sampling Distribution
The variance of a random variable
A probability density function
Statistical adjustment
43. 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
Ratio measurements
P-value
Observational study
That is the median value
44. Failing to reject a false null hypothesis.
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Credence
An estimate of a parameter
Type 2 Error
45. Is the most commonly used measure of statistical dispersion. It is the square root of the variance - and is generally written s (sigma).
Greek letters
categorical variables
Pairwise independence
The standard deviation
46. 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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47. Is the result of applying a statistical algorithm to a data set. It can also be described as an observable random variable.
An experimental study
expected value of X
A statistic
Probability density
48. (also called statistical variability) is a measure of how diverse some data is. It can be expressed by the variance or the standard deviation.
A Random vector
An Elementary event
Statistical dispersion
the population variance
49. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Pairwise independence
A data set
Sampling Distribution
50. ?
covariance of X and Y
the population correlation
Estimator
Descriptive statistics