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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. 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.
Marginal distribution
Coefficient of determination
Binomial experiment
That value is the median value
2. Is a parameter that indexes a family of probability distributions.
Observational study
Descriptive statistics
A sampling distribution
A Statistical parameter
3. Descriptive statistics and inferential statistics (a.k.a. - predictive statistics) together comprise
A probability space
Atomic event
The Range
applied statistics
4. 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}.
the population variance
Lurking variable
The sample space
Conditional distribution
5. Cov[X - Y] :
Kurtosis
The average - or arithmetic mean
covariance of X and Y
Bias
6. 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.
Greek letters
Kurtosis
Bias
hypotheses
7. Is defined as the expected value of random variable (X -
Statistics
Block
The variance of a random variable
The Covariance between two random variables X and Y - with expected values E(X) =
8. A consistent - repeated deviation of the sample statistic from the population parameter in the same direction when many samples are taken.
Divide the sum by the number of values.
Sample space
Bias
A data set
9. 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.
The Covariance between two random variables X and Y - with expected values E(X) =
A probability space
Type II errors
A data point
10. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
Block
Pairwise independence
Sampling Distribution
Beta value
11. Data are gathered and correlations between predictors and response are investigated.
observational study
Ratio measurements
A sampling distribution
Type 2 Error
12. 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.
quantitative variables
Qualitative variable
Lurking variable
Kurtosis
13. 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
methods of least squares
Joint distribution
Step 3 of a statistical experiment
14. Is the function that gives the probability distribution of a random variable. It cannot be negative - and its integral on the probability space is equal to 1.
Credence
A Distribution function
Ordinal measurements
Sampling
15. A measure that is relevant or appropriate as a representation of that property.
A sampling distribution
Interval measurements
Statistics
Valid measure
16. 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
Probability
Independence or Statistical independence
Probability density functions
Step 3 of a statistical experiment
17. In particular - the pdf of the standard normal distribution is denoted by
f(z) - and its cdf by F(z).
Confounded variables
Kurtosis
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
18. Some commonly used symbols for sample statistics
A Statistical parameter
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Alpha value (Level of Significance)
Ratio measurements
19. 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.
Prior probability
Beta value
Statistics
Sample space
20. 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.
hypotheses
Reliable measure
Alpha value (Level of Significance)
Dependent Selection
21. Var[X] :
methods of least squares
applied statistics
Conditional probability
variance of X
22. Statistics involve methods of using information from a sample to draw conclusions regarding the population.
Inferential
Variability
A probability distribution
Observational study
23. Describes a characteristic of an individual to be measured or observed.
the population cumulants
Variable
An experimental study
Cumulative distribution functions
24. 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 median value
Joint probability
Type I errors & Type II errors
Type I errors
25. Is data that can take only two values - usually represented by 0 and 1.
Binary data
quantitative variables
Block
Independence or Statistical independence
26. Is denoted by - pronounced 'x bar'.
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
An event
hypothesis
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
27. To find the average - or arithmetic mean - of a set of numbers:
Conditional distribution
Count data
Divide the sum by the number of values.
the population mean
28. 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.
Treatment
Sampling frame
Experimental and observational studies
That value is the median value
29. A measurement such that the random error is small
The sample space
Type 2 Error
The Mean of a random variable
Reliable measure
30. Failing to reject a false null hypothesis.
Experimental and observational studies
Type 2 Error
The Mean of a random variable
Independent Selection
31. ?
the population correlation
Observational study
the population mean
inferential statistics
32. The objects described by a set of data: person (animal) - place - and - thing. (SUBJECTS)
The Range
Pairwise independence
Individual
The variance of a random variable
33. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
Law of Large Numbers
Dependent Selection
Divide the sum by the number of values.
Nominal measurements
34. The standard deviation of a sampling distribution.
Count data
s-algebras
Standard error
Variable
35. 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
Skewness
inferential statistics
the population mean
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
36. The proportion of the explained variation by a linear regression model in the total variation.
Pairwise independence
Coefficient of determination
Statistical dispersion
Treatment
37. When you have two or more competing models - choose the simpler of the two models.
Mutual independence
A statistic
variance of X
Law of Parsimony
38. Are simply two different terms for the same thing. Add the given values
Parameter
Average and arithmetic mean
Experimental and observational studies
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
39. A scale that represents an ordinal scale such as looks on a scale from 1 to 10.
Atomic event
Likert scale
The Covariance between two random variables X and Y - with expected values E(X) =
Step 3 of a statistical experiment
40. (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 population correlation
Probability and statistics
A probability distribution
An Elementary event
41. 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
Statistical dispersion
A sample
Step 1 of a statistical experiment
Type I errors
42. Any specific experimental condition applied to the subjects
Lurking variable
Treatment
A random variable
Likert scale
43. 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
Joint probability
expected value of X
Probability density
The Covariance between two random variables X and Y - with expected values E(X) =
44. Is a function of the known data that is used to estimate an unknown parameter; an estimate is the result from the actual application of the function to a particular set of data. The mean can be used as an estimator.
Ordinal measurements
Estimator
Observational study
The Mean of a random variable
45. A numerical measure that describes an aspect of a sample.
Experimental and observational studies
Statistics
Statistic
the population variance
46. 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
Binary data
Statistical dispersion
Step 2 of a statistical experiment
inferential statistics
47. Ratio and interval measurements which can be either discrete or continuous - due to their numerical nature are grouped together as
quantitative variables
A Statistical parameter
covariance of X and Y
Statistics
48. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
A sampling distribution
the population mean
An Elementary event
Pairwise independence
49. Some commonly used symbols for population parameters
Simulation
Individual
The standard deviation
the population mean
50. A numerical measure that describes an aspect of a population.
A sample
Descriptive statistics
Parameter
A statistic