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Test your basic knowledge |
CLEP General Mathematics: Probability And Statistics
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Study First
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. Is denoted by - pronounced 'x bar'.
Prior probability
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Simulation
Mutual independence
2. 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.
The Range
Joint distribution
The standard deviation
That value is the median value
3. 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'
Coefficient of determination
Conditional probability
expected value of X
Probability
4. 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
The Mean of a random variable
the sample or population mean
An Elementary event
Independence or Statistical independence
5. Cov[X - Y] :
Parameter - or 'statistical parameter'
covariance of X and Y
The sample space
Quantitative variable
6. Data are gathered and correlations between predictors and response are investigated.
Sampling
Beta value
A data set
observational study
7. 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
Valid measure
Binomial experiment
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
8. To find the average - or arithmetic mean - of a set of numbers:
Descriptive
Divide the sum by the number of values.
Law of Large Numbers
A data point
9. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
Posterior probability
The Mean of a random variable
Parameter - or 'statistical parameter'
Law of Large Numbers
10. (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
Step 1 of a statistical experiment
An Elementary event
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
11. (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
Parameter - or 'statistical parameter'
The Expected value
Power of a test
Prior probability
12. A numerical measure that describes an aspect of a sample.
Mutual independence
Independence or Statistical independence
Beta value
Statistic
13. 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.
The variance of a random variable
descriptive statistics
Statistical inference
Probability and statistics
14. A scale that represents an ordinal scale such as looks on a scale from 1 to 10.
Type I errors
That is the median value
Likert scale
Joint probability
15. S^2
Probability and statistics
Average and arithmetic mean
the population variance
Null hypothesis
16.
Trend
Interval measurements
That value is the median value
the population mean
17. Describes the spread in the values of the sample statistic when many samples are taken.
Variability
Law of Parsimony
Variable
Confounded variables
18. A data value that falls outside the overall pattern of the graph.
A Distribution function
An experimental study
Outlier
the population mean
19. Have imprecise differences between consecutive values - but have a meaningful order to those values
Ordinal measurements
Kurtosis
Inferential statistics
the population cumulants
20. 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
Individual
Marginal distribution
Descriptive statistics
Independent Selection
21. Is a parameter that indexes a family of probability distributions.
A Statistical parameter
observational study
Observational study
the population mean
22. A common goal for a statistical research project is to investigate causality - and in particular to draw a conclusion on the effect of changes in the values of predictors or independent variables on dependent variables or response.
descriptive statistics
Experimental and observational studies
Type II errors
A statistic
23. Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically - sometimes they are grouped together as
Type I errors
Variability
categorical variables
Type II errors
24. There are two major types of causal statistical studies: In both types of studies - the effect of differences of an independent variable (or variables) on the behavior of the dependent variable are observed. The difference between the two types lies
Simulation
An Elementary event
experimental studies and observational studies.
The Range
25. Failing to reject a false null hypothesis.
Type 2 Error
Likert scale
Marginal probability
Binomial experiment
26. 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.
Statistics
A probability density function
Correlation coefficient
Simple random sample
27. ?
A Random vector
Experimental and observational studies
the population correlation
expected value of X
28. Some commonly used symbols for population parameters
Type I errors & Type II errors
Ratio measurements
the population mean
Statistical dispersion
29. Is a sample and the associated data points.
A data set
Treatment
A probability space
observational study
30. Is the length of the smallest interval which contains all the data.
The Range
The median value
Kurtosis
A probability distribution
31. Is used to describe probability in a continuous probability distribution. For example - you can't say that the probability of a man being six feet tall is 20% - but you can say he has 20% of chances of being between five and six feet tall. Probabilit
Probability density
A population or statistical population
A probability space
The Covariance between two random variables X and Y - with expected values E(X) =
32. Describes a characteristic of an individual to be measured or observed.
Step 2 of a statistical experiment
Marginal probability
Prior probability
Variable
33. Any specific experimental condition applied to the subjects
expected value of X
Law of Parsimony
Simulation
Treatment
34. Are usually written with upper case calligraphic (e.g. F for the set of sets on which we define the probability P)
nominal - ordinal - interval - and ratio
The average - or arithmetic mean
s-algebras
The Range
35. Is that part of a population which is actually observed.
A sample
Variability
A probability density function
Step 1 of a statistical experiment
36. Many statistical methods seek to minimize the mean-squared error - and these are called
methods of least squares
Particular realizations of a random variable
A probability space
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
37. Ratio and interval measurements which can be either discrete or continuous - due to their numerical nature are grouped together as
Independence or Statistical independence
P-value
s-algebras
quantitative variables
38. (pdfs) and probability mass functions are denoted by lower case letters - e.g. f(x).
hypothesis
Probability density functions
Parameter - or 'statistical parameter'
Mutual independence
39. Statistics involve methods of using information from a sample to draw conclusions regarding the population.
Statistical dispersion
A probability space
Independence or Statistical independence
Inferential
40. Statistical methods can be used for summarizing or describing a collection of data; this is called
Power of a test
The Expected value
descriptive statistics
Outlier
41. (or multivariate random variable) is a vector whose components are random variables on the same probability space.
Inferential statistics
hypotheses
A Random vector
Bias
42. A group of individuals sharing some common features that might affect the treatment.
Seasonal effect
Block
Type I errors
Simulation
43. 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.
the population mean
Statistics
the sample or population mean
Treatment
44. A numerical measure that describes an aspect of a population.
the population correlation
covariance of X and Y
Parameter
A sampling distribution
45. 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 cumulants
The median value
An Elementary event
Type II errors
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
An event
Lurking variable
Skewness
A Random vector
47. Is the result of applying a statistical algorithm to a data set. It can also be described as an observable random variable.
A statistic
Inferential
A probability space
The variance of a random variable
48. 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.
A sample
Step 3 of a statistical experiment
Kurtosis
Statistic
49. Is the probability distribution - under repeated sampling of the population - of a given statistic.
Independent Selection
A sampling distribution
The average - or arithmetic mean
Placebo effect
50. 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.
Type II errors
An experimental study
Type I errors & Type II errors
the population mean