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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.
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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. To prove the guiding theory further - these predictions are tested as well - as part of the scientific method. If the inference holds true - then the descriptive statistics of the new data increase the soundness of that
Descriptive
hypothesis
Statistical dispersion
A statistic
2. Is a subset of the sample space - to which a probability can be assigned. For example - on rolling a die - 'getting a five or a six' is an event (with a probability of one third if the die is fair).
Pairwise independence
An event
A population or statistical population
Skewness
3. 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.
Credence
Statistical inference
Dependent Selection
The median value
4. (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.
A probability space
Marginal distribution
Block
An Elementary event
5. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
Sampling Distribution
covariance of X and Y
the population mean
Independent Selection
6. 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
Random variables
Lurking variable
Binary data
Skewness
7. Ratio and interval measurements which can be either discrete or continuous - due to their numerical nature are grouped together as
Greek letters
Type I errors
quantitative variables
Confounded variables
8. Is the most commonly used measure of statistical dispersion. It is the square root of the variance - and is generally written s (sigma).
Mutual independence
An Elementary event
Experimental and observational studies
The standard deviation
9. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.
An estimate of a parameter
Joint distribution
experimental studies and observational studies.
hypotheses
10. Is data that can take only two values - usually represented by 0 and 1.
Binary data
The variance of a random variable
A Random vector
Cumulative distribution functions
11. A numerical measure that describes an aspect of a sample.
Statistic
variance of X
A probability space
observational study
12. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
Prior probability
Placebo effect
Statistic
Quantitative variable
13. Is denoted by - pronounced 'x bar'.
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Seasonal effect
The variance of a random variable
Probability density
14. Is a sample space over which a probability measure has been defined.
Cumulative distribution functions
A Probability measure
Type II errors
A probability space
15. Are written in corresponding lower case letters. For example x1 - x2 - ... - xn could be a sample corresponding to the random variable X.
observational study
Descriptive statistics
Divide the sum by the number of values.
Particular realizations of a random variable
16. 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.
Probability
Power of a test
A Statistical parameter
Lurking variable
17. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
inferential statistics
Lurking variable
Binomial experiment
nominal - ordinal - interval - and ratio
18. 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.
Dependent Selection
Type II errors
Simple random sample
An experimental study
19. Another name for elementary event.
Atomic event
Variability
Statistical adjustment
Type II errors
20. A variable describes an individual by placing the individual into a category or a group.
Count data
Qualitative variable
Confounded variables
The sample space
21. Rejecting a true null hypothesis.
Type 1 Error
A probability density function
A population or statistical population
Parameter - or 'statistical parameter'
22. 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).
A probability density function
Joint probability
Type I errors & Type II errors
Sampling
23. 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.
The sample space
Joint probability
A population or statistical population
observational study
24. Used to reduce bias - this measure weights the more relevant information higher than less relevant info.
Type 2 Error
Nominal measurements
Statistical adjustment
Binomial experiment
25. Is that part of a population which is actually observed.
Statistic
A sample
The Covariance between two random variables X and Y - with expected values E(X) =
Probability density
26. Is its expected value. The mean (or sample mean of a data set is just the average value.
Probability density functions
the sample or population mean
The Mean of a random variable
s-algebras
27. When info. in a contingency table is re-organized into more or less categories - relationships seen can change or reverse.
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28. A data value that falls outside the overall pattern of the graph.
inferential statistics
Independence or Statistical independence
Outlier
The average - or arithmetic mean
29. Is a function that gives the probability of all elements in a given space: see List of probability distributions
A probability distribution
Independent Selection
Sampling
Joint probability
30. Many statistical methods seek to minimize the mean-squared error - and these are called
Greek letters
methods of least squares
Joint distribution
Quantitative variable
31. Is the result of applying a statistical algorithm to a data set. It can also be described as an observable random variable.
Placebo effect
A likelihood function
Simpson's Paradox
A statistic
32. Is one that explores the correlation between smoking and lung cancer. This type of study typically uses a survey to collect observations about the area of interest and then performs statistical analysis. In this case - the researchers would collect o
Type 1 Error
Beta value
Observational study
Lurking variable
33. A scale that represents an ordinal scale such as looks on a scale from 1 to 10.
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
A probability distribution
Likert scale
Outlier
34. Any specific experimental condition applied to the subjects
Step 3 of a statistical experiment
That is the median value
Treatment
The Covariance between two random variables X and Y - with expected values E(X) =
35. Occurs when a subject receives no treatment - but (incorrectly) believes he or she is in fact receiving treatment and responds favorably.
the population mean
Type I errors & Type II errors
Placebo effect
Type 2 Error
36. (or multivariate random variable) is a vector whose components are random variables on the same probability space.
A likelihood function
A Random vector
the population mean
hypotheses
37. To find the average - or arithmetic mean - of a set of numbers:
Pairwise independence
Sampling Distribution
Divide the sum by the number of values.
Descriptive statistics
38. Descriptive statistics and inferential statistics (a.k.a. - predictive statistics) together comprise
A Probability measure
Null hypothesis
Particular realizations of a random variable
applied statistics
39. Have no meaningful rank order among values.
Particular realizations of a random variable
Nominal measurements
Law of Parsimony
Type I errors & Type II errors
40. Statistical methods can be used for summarizing or describing a collection of data; this is called
A population or statistical population
An Elementary event
Experimental and observational studies
descriptive statistics
41. 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.
the sample or population mean
A data set
Descriptive
Kurtosis
42. 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.
Pairwise independence
Statistics
Law of Parsimony
The sample space
43. ?
Bias
Variable
Trend
the population correlation
44. When you have two or more competing models - choose the simpler of the two models.
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Cumulative distribution functions
Law of Parsimony
Correlation
45. 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
A Random vector
Joint probability
Alpha value (Level of Significance)
Probability
46. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
s-algebras
P-value
Inferential
Law of Parsimony
47. Is a typed measurement - it can be a boolean value - a real number - a vector (in which case it's also called a data vector) - etc.
Likert scale
A data point
experimental studies and observational studies.
Sample space
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.
Simple random sample
Statistics
Statistical dispersion
A likelihood function
49. 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
Sample space
Inferential statistics
The variance of a random variable
quantitative variables
50. 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.
A random variable
Probability density functions
Confounded variables
Nominal measurements