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Test your basic knowledge |
CLEP General Mathematics: Probability And Statistics
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clep
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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
hypothesis
observational study
Block
the population cumulants
2. (cdfs) are denoted by upper case letters - e.g. F(x).
Cumulative distribution functions
Atomic event
Law of Large Numbers
A random variable
3. 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.
Statistical dispersion
Simple random sample
Cumulative distribution functions
Type I errors & Type II errors
4. Describes a characteristic of an individual to be measured or observed.
Conditional distribution
Variable
Observational study
Kurtosis
5. Is a function that gives the probability of all elements in a given space: see List of probability distributions
Ordinal measurements
descriptive statistics
A probability distribution
Sample space
6. A consistent - repeated deviation of the sample statistic from the population parameter in the same direction when many samples are taken.
variance of X
quantitative variables
Bias
The standard deviation
7. 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
Independence or Statistical independence
Cumulative distribution functions
applied statistics
The Mean of a random variable
8. Some commonly used symbols for population parameters
The Mean of a random variable
Sampling Distribution
the population mean
The Covariance between two random variables X and Y - with expected values E(X) =
9. 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.
A Probability measure
Simulation
observational study
Bias
10. Is the most commonly used measure of statistical dispersion. It is the square root of the variance - and is generally written s (sigma).
A data point
quantitative variables
Particular realizations of a random variable
The standard deviation
11. Consists of a number of independent trials repeated under identical conditions. On each trial - there are two possible outcomes.
Binomial experiment
A Distribution function
Simple random sample
A Probability measure
12. Are usually written in upper case roman letters: X - Y - etc.
The variance of a random variable
A probability distribution
Parameter - or 'statistical parameter'
Random variables
13. Var[X] :
variance of X
Mutual independence
Qualitative variable
Probability density functions
14. Any specific experimental condition applied to the subjects
Treatment
Type 2 Error
Atomic event
Nominal measurements
15. Working from a null hypothesis two basic forms of error are recognized:
Type I errors & Type II errors
Placebo effect
Descriptive
Type 2 Error
16. 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.
Experimental and observational studies
experimental studies and observational studies.
A population or statistical population
Beta value
17. Given two jointly distributed random variables X and Y - the conditional probability distribution of Y given X (written 'Y | X') is the probability distribution of Y when X is known to be a particular value.
Power of a test
Skewness
Conditional distribution
Posterior probability
18. Is the probability of an event - ignoring any information about other events. The marginal probability of A is written P(A). Contrast with conditional probability.
Experimental and observational studies
Marginal probability
Statistical dispersion
Probability
19. When info. in a contingency table is re-organized into more or less categories - relationships seen can change or reverse.
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20. A collection of events is mutually independent if for any subset of the collection - the joint probability of all events occurring is equal to the product of the joint probabilities of the individual events. Think of the result of a series of coin-fl
Mutual independence
A data point
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Inferential statistics
21. Ratio and interval measurements which can be either discrete or continuous - due to their numerical nature are grouped together as
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Sample space
methods of least squares
quantitative variables
22. 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.
categorical variables
A random variable
Step 2 of a statistical experiment
Marginal probability
23. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.
Statistical dispersion
An estimate of a parameter
An event
Statistical adjustment
24. When there is an even number of values...
Step 2 of a statistical experiment
f(z) - and its cdf by F(z).
That is the median value
Ratio measurements
25. Rejecting a true null hypothesis.
Bias
Probability
Type 1 Error
the population variance
26. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
Pairwise independence
Statistics
Quantitative variable
covariance of X and Y
27. Probability of rejecting a true null hypothesis.
Alpha value (Level of Significance)
Average and arithmetic mean
Variability
Probability density functions
28. The collection of all possible outcomes in an experiment.
Sample space
The Mean of a random variable
Step 3 of a statistical experiment
Bias
29. A variable has a value or numerical measurement for which operations such as addition or averaging make sense.
Binary data
An Elementary event
The Range
Quantitative variable
30. Performing the experiment following the experimental protocol and analyzing the data following the experimental protocol. 4. Further examining the data set in secondary analyses - to suggest new hypotheses for future study. 5. Documenting and present
Statistical dispersion
nominal - ordinal - interval - and ratio
hypothesis
Step 3 of a statistical experiment
31. A data value that falls outside the overall pattern of the graph.
Descriptive
An Elementary event
A Probability measure
Outlier
32. Data are gathered and correlations between predictors and response are investigated.
the population mean
Prior probability
Standard error
observational study
33. A numerical measure that describes an aspect of a population.
Atomic event
Divide the sum by the number of values.
Descriptive
Parameter
34. 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
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Probability
Binomial experiment
Independent Selection
35. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
A sample
A data set
methods of least squares
P-value
36. Occurs when a subject receives no treatment - but (incorrectly) believes he or she is in fact receiving treatment and responds favorably.
That value is the median value
the population cumulants
Placebo effect
hypotheses
37. Is a parameter that indexes a family of probability distributions.
A probability distribution
The Expected value
the population cumulants
A Statistical parameter
38. 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.
Block
the sample or population mean
observational study
Sampling
39. Is denoted by - pronounced 'x bar'.
Independence or Statistical independence
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Valid measure
Binomial experiment
40. Gives the probability of events in a probability space.
hypothesis
Trend
A Probability measure
Coefficient of determination
41. ?r
A Statistical parameter
covariance of X and Y
Simple random sample
the population cumulants
42. 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
Block
The variance of a random variable
Skewness
Quantitative variable
43. Cov[X - Y] :
covariance of X and Y
Type I errors & Type II errors
The average - or arithmetic mean
Simple random sample
44. E[X] :
Quantitative variable
Residuals
expected value of X
Coefficient of determination
45. 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.
Seasonal effect
Qualitative variable
A probability space
Marginal distribution
46. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
quantitative variables
A Probability measure
Prior probability
Conditional probability
47. Where the null hypothesis is falsely rejected giving a 'false positive'.
Marginal distribution
Type I errors
An Elementary event
Statistics
48. 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.
Statistics
Probability and statistics
Inferential statistics
Nominal measurements
49. Are written in corresponding lower case letters. For example x1 - x2 - ... - xn could be a sample corresponding to the random variable X.
Reliable measure
the sample or population mean
The standard deviation
Particular realizations of a random variable
50. The result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data
Qualitative variable
Type I errors & Type II errors
Posterior probability
A statistic