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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. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.
A sampling distribution
An estimate of a parameter
Pairwise independence
P-value
2. To find the average - or arithmetic mean - of a set of numbers:
Joint probability
Skewness
Divide the sum by the number of values.
Statistical adjustment
3. A numerical measure that assesses the strength of a linear relationship between two variables.
Binomial experiment
Atomic event
Correlation coefficient
variance of X
4. 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.
Outlier
Marginal distribution
Simulation
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
5. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively
A population or statistical population
The Range
The Mean of a random variable
Residuals
6. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
Step 1 of a statistical experiment
hypothesis
Cumulative distribution functions
Pairwise independence
7. Is the probability of some event A - assuming event B. Conditional probability is written P(A|B) - and is read 'the probability of A - given B'
Type II errors
Statistical adjustment
Conditional probability
The variance of a random variable
8. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
The Expected value
applied statistics
Sampling Distribution
An experimental study
9. Working from a null hypothesis two basic forms of error are recognized:
categorical variables
The standard deviation
Law of Large Numbers
Type I errors & Type II errors
10. 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
Descriptive statistics
Sampling Distribution
Nominal measurements
Statistic
11. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.
Descriptive
Statistical adjustment
Alpha value (Level of Significance)
the population correlation
12. Gives the probability distribution for a continuous random variable.
Descriptive
Trend
Reliable measure
A probability density function
13. Another name for elementary event.
That is the median value
s-algebras
Marginal distribution
Atomic event
14. 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.
Step 2 of a statistical experiment
A data point
Statistics
Block
15. A scale that represents an ordinal scale such as looks on a scale from 1 to 10.
Law of Parsimony
A data point
Posterior probability
Likert scale
16. Planning the research - including finding the number of replicates of the study - using the following information: preliminary estimates regarding the size of treatment effects - alternative hypotheses - and the estimated experimental variability. Co
Step 1 of a statistical experiment
Ordinal measurements
Sampling
A data set
17. The objects described by a set of data: person (animal) - place - and - thing. (SUBJECTS)
Type II errors
Residuals
Individual
A Distribution function
18. (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
A likelihood function
Standard error
Conditional probability
A probability distribution
19. Describes a characteristic of an individual to be measured or observed.
A data point
Type I errors
Variable
Step 1 of a statistical experiment
20. The collection of all possible outcomes in an experiment.
That is the median value
Trend
Sample space
Power of a test
21. 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
Marginal probability
Ratio measurements
Random variables
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
22. Is a function that gives the probability of all elements in a given space: see List of probability distributions
Lurking variable
A probability distribution
A Probability measure
Standard error
23. A data value that falls outside the overall pattern of the graph.
Ratio measurements
Outlier
A Distribution function
The median value
24. Many statistical methods seek to minimize the mean-squared error - and these are called
expected value of X
methods of least squares
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Skewness
25. Is a parameter that indexes a family of probability distributions.
The Range
That value is the median value
A Statistical parameter
Divide the sum by the number of values.
26. Rejecting a true null hypothesis.
The Range
Type 1 Error
Joint distribution
Probability density functions
27. Cov[X - Y] :
covariance of X and Y
s-algebras
Prior probability
Valid measure
28. Two variables such that their effects on the response variable cannot be distinguished from each other.
A sampling distribution
hypothesis
Confounded variables
Alpha value (Level of Significance)
29. 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.
Descriptive
hypotheses
Observational study
Sampling
30. A variable has a value or numerical measurement for which operations such as addition or averaging make sense.
Ratio measurements
Quantitative variable
variance of X
Correlation coefficient
31. The probability of correctly detecting a false null hypothesis.
descriptive statistics
The sample space
A Probability measure
Power of a test
32. 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.
Statistical inference
A population or statistical population
Quantitative variable
Step 3 of a statistical experiment
33. 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 population mean
Inferential
Qualitative variable
Step 2 of a statistical experiment
34. When there is an even number of values...
Conditional distribution
covariance of X and Y
Statistical adjustment
That is the median value
35. The proportion of the explained variation by a linear regression model in the total variation.
Credence
the population cumulants
The sample space
Coefficient of determination
36. 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
inferential statistics
categorical variables
Step 2 of a statistical experiment
the sample or population mean
37. (pdfs) and probability mass functions are denoted by lower case letters - e.g. f(x).
Probability and statistics
A Random vector
Probability density functions
The Covariance between two random variables X and Y - with expected values E(X) =
38. Also called correlation coefficient - is a numeric measure of the strength of linear relationship between two random variables (one can use it to quantify - for example - how shoe size and height are correlated in the population). An example is the P
Quantitative variable
Correlation
A data point
Type II errors
39. Where the null hypothesis fails to be rejected and an actual difference between populations is missed giving a 'false negative'.
Type II errors
Dependent Selection
Step 1 of a statistical experiment
Probability density
40. 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.
Simpson's Paradox
A random variable
observational study
experimental studies and observational studies.
41. A list of individuals from which the sample is actually selected.
hypotheses
Statistical inference
Sampling frame
Simpson's Paradox
42. S^2
A random variable
Conditional probability
the population variance
Quantitative variable
43. Have imprecise differences between consecutive values - but have a meaningful order to those values
Marginal probability
the population mean
Ordinal measurements
Particular realizations of a random variable
44. A measure that is relevant or appropriate as a representation of that property.
Valid measure
s-algebras
Inferential
The sample space
45. Is the result of applying a statistical algorithm to a data set. It can also be described as an observable random variable.
Independent Selection
A statistic
Trend
Lurking variable
46. 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
A random variable
Binomial experiment
Skewness
Prior probability
47. Statistical methods can be used for summarizing or describing a collection of data; this is called
descriptive statistics
Probability
Mutual independence
Divide the sum by the number of values.
48. 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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49. 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.
Likert scale
Probability density functions
An experimental study
Alpha value (Level of Significance)
50. (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.
Law of Large Numbers
Mutual independence
An Elementary event
The variance of a random variable