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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. 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.
2. Two variables such that their effects on the response variable cannot be distinguished from each other.
An estimate of a parameter
Confounded variables
Pairwise independence
Particular realizations of a random variable
3. Some commonly used symbols for population parameters
Sampling frame
Statistic
The variance of a random variable
the population mean
4. Long-term upward or downward movement over time.
An experimental study
nominal - ordinal - interval - and ratio
Trend
expected value of X
5. Describes a characteristic of an individual to be measured or observed.
Variable
A probability space
A population or statistical population
An experimental study
6. A numerical measure that describes an aspect of a sample.
Statistic
Outlier
Average and arithmetic mean
Credence
7. A variable has a value or numerical measurement for which operations such as addition or averaging make sense.
Interval measurements
Quantitative variable
Step 2 of a statistical experiment
Beta value
8. (pdfs) and probability mass functions are denoted by lower case letters - e.g. f(x).
descriptive statistics
Dependent Selection
Probability density functions
Atomic event
9. 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
the sample or population mean
Sampling frame
Type 2 Error
hypotheses
10. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
Alpha value (Level of Significance)
Credence
Statistic
Prior probability
11. Is the length of the smallest interval which contains all the data.
The Range
That is the median value
A Distribution function
Observational study
12. Is denoted by - pronounced 'x bar'.
The variance of a random variable
Binary data
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Probability
13. 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.
That value is the median value
Law of Parsimony
Estimator
Interval measurements
14. 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
Step 2 of a statistical experiment
An estimate of a parameter
Particular realizations of a random variable
15. 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.
Kurtosis
A sampling distribution
Dependent Selection
Type 2 Error
16. Var[X] :
The Expected value
variance of X
Kurtosis
A random variable
17. Probability of rejecting a true null hypothesis.
covariance of X and Y
Binomial experiment
categorical variables
Alpha value (Level of Significance)
18. 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
Simple random sample
Skewness
inferential statistics
A sampling distribution
19. Is a sample and the associated data points.
The Range
Count data
A data set
Experimental and observational studies
20. 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.
The variance of a random variable
hypothesis
Quantitative variable
A random variable
21. A numerical measure that assesses the strength of a linear relationship between two variables.
Outlier
Parameter - or 'statistical parameter'
Correlation coefficient
the population mean
22. Samples are drawn from two different populations such that the sample data drawn from one population is completely unrelated to the selection of sample data from the other population.
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Placebo effect
Marginal distribution
Independent Selection
23. Have imprecise differences between consecutive values - but have a meaningful order to those values
A likelihood function
descriptive statistics
Ordinal measurements
Alpha value (Level of Significance)
24. Is a function that gives the probability of all elements in a given space: see List of probability distributions
hypothesis
Standard error
Dependent Selection
A probability distribution
25. Working from a null hypothesis two basic forms of error are recognized:
Treatment
Type I errors & Type II errors
Parameter - or 'statistical parameter'
Confounded variables
26. Some commonly used symbols for sample statistics
s-algebras
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
descriptive statistics
inferential statistics
27. 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.
Power of a test
Seasonal effect
Skewness
Mutual independence
28. 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}.
Coefficient of determination
The sample space
Likert scale
Null hypothesis
29. 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).
Experimental and observational studies
Parameter - or 'statistical parameter'
Variability
Joint probability
30. Is defined as the expected value of random variable (X -
Type 1 Error
That value is the median value
A Random vector
The Covariance between two random variables X and Y - with expected values E(X) =
31. 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
A Distribution function
Outlier
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
32. A measure that is relevant or appropriate as a representation of that property.
Ratio measurements
Valid measure
The Mean of a random variable
Null hypothesis
33. Is data arising from counting that can take only non-negative integer values.
Count data
Standard error
Simpson's Paradox
Parameter
34. To find the average - or arithmetic mean - of a set of numbers:
The sample space
Divide the sum by the number of values.
The variance of a random variable
Estimator
35. (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
A likelihood function
The Expected value
Estimator
The average - or arithmetic mean
36. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively
An experimental study
A Distribution function
Residuals
Binomial experiment
37. The result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data
Independence or Statistical independence
Posterior probability
Simulation
Reliable measure
38. Are usually written with upper case calligraphic (e.g. F for the set of sets on which we define the probability P)
Type 2 Error
Interval measurements
Step 3 of a statistical experiment
s-algebras
39. Is a set of entities about which statistical inferences are to be drawn - often based on random sampling. One can also talk about a population of measurements or values.
A likelihood function
Bias
A population or statistical population
Qualitative variable
40. Is a parameter that indexes a family of probability distributions.
nominal - ordinal - interval - and ratio
the population mean
A statistic
A Statistical parameter
41. (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.
The median value
Type 2 Error
An Elementary event
Binary data
42. 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.
Law of Large Numbers
Sampling
A Distribution function
A data set
43. 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.
Ratio measurements
The variance of a random variable
An estimate of a parameter
Placebo effect
44. A scale that represents an ordinal scale such as looks on a scale from 1 to 10.
Type II errors
Quantitative variable
Likert scale
Probability density functions
45. 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
Treatment
That value is the median value
Simple random sample
46. 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'
Parameter - or 'statistical parameter'
Qualitative variable
Conditional probability
A Probability measure
47. A subjective estimate of probability.
Credence
Bias
observational study
A sampling distribution
48. Used to reduce bias - this measure weights the more relevant information higher than less relevant info.
Divide the sum by the number of values.
Block
Correlation coefficient
Statistical adjustment
49. 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.
Cumulative distribution functions
Law of Large Numbers
Posterior probability
Statistics
50. Given two random variables X and Y - the joint distribution of X and Y is the probability distribution of X and Y together.
An estimate of a parameter
Joint distribution
Correlation
Power of a test