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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. The standard deviation of a sampling distribution.
Standard error
Beta value
Variable
A Probability measure
2. Two variables such that their effects on the response variable cannot be distinguished from each other.
A probability space
Confounded variables
Qualitative variable
Parameter
3. 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
Valid measure
Independent Selection
Correlation
4. 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.
Descriptive
Sampling
Power of a test
A sample
5. The collection of all possible outcomes in an experiment.
An estimate of a parameter
Sampling
Binary data
Sample space
6. Cov[X - Y] :
nominal - ordinal - interval - and ratio
the population mean
covariance of X and Y
Sample space
7. A variable has a value or numerical measurement for which operations such as addition or averaging make sense.
Quantitative variable
Sampling Distribution
Variability
Statistical inference
8. Used to reduce bias - this measure weights the more relevant information higher than less relevant info.
Statistical adjustment
Greek letters
Count data
the population mean
9. (also called statistical variability) is a measure of how diverse some data is. It can be expressed by the variance or the standard deviation.
Inferential statistics
The standard deviation
methods of least squares
Statistical dispersion
10. 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.
Marginal probability
Divide the sum by the number of values.
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
variance of X
11. Consists of a number of independent trials repeated under identical conditions. On each trial - there are two possible outcomes.
Joint distribution
Binomial experiment
A Random vector
Parameter
12. Is a sample space over which a probability measure has been defined.
the population cumulants
The average - or arithmetic mean
A probability space
Simple random sample
13. 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.
Statistics
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Simpson's Paradox
A data point
14. A data value that falls outside the overall pattern of the graph.
The average - or arithmetic mean
A likelihood function
Outlier
f(z) - and its cdf by F(z).
15. Where the null hypothesis is falsely rejected giving a 'false positive'.
Experimental and observational studies
An experimental study
Correlation coefficient
Type I errors
16. Descriptive statistics and inferential statistics (a.k.a. - predictive statistics) together comprise
Nominal measurements
applied statistics
Coefficient of determination
Sampling frame
17. 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 standard deviation
That value is the median value
Marginal distribution
Inferential statistics
18. Are usually written in upper case roman letters: X - Y - etc.
Random variables
A data set
A population or statistical population
The Range
19. 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.
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20. Is a sample and the associated data points.
Greek letters
A data set
Mutual independence
categorical variables
21. A variable describes an individual by placing the individual into a category or a group.
Kurtosis
Qualitative variable
Type 1 Error
An event
22. In particular - the pdf of the standard normal distribution is denoted by
descriptive statistics
A likelihood function
An event
f(z) - and its cdf by F(z).
23. Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically - sometimes they are grouped together as
The variance of a random variable
categorical variables
The Expected value
A data point
24. Var[X] :
Parameter
Joint probability
An Elementary event
variance of X
25. Is a parameter that indexes a family of probability distributions.
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
A population or statistical population
Random variables
A Statistical parameter
26. 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.
That is the median value
Step 1 of a statistical experiment
Probability and statistics
Bias
27. Is data arising from counting that can take only non-negative integer values.
Correlation
Count data
Conditional distribution
nominal - ordinal - interval - and ratio
28. 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 Covariance between two random variables X and Y - with expected values E(X) =
Kurtosis
Alpha value (Level of Significance)
s-algebras
29. Is the result of applying a statistical algorithm to a data set. It can also be described as an observable random variable.
Atomic event
Block
Statistical adjustment
A statistic
30. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
the sample or population mean
A Distribution function
A population or statistical population
nominal - ordinal - interval - and ratio
31. Ratio and interval measurements which can be either discrete or continuous - due to their numerical nature are grouped together as
Descriptive
quantitative variables
Atomic event
inferential statistics
32. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.
An event
Descriptive
The average - or arithmetic mean
observational study
33. To find the average - or arithmetic mean - of a set of numbers:
Descriptive statistics
Divide the sum by the number of values.
A population or statistical population
The average - or arithmetic mean
34. Is denoted by - pronounced 'x bar'.
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
A random variable
the population mean
Greek letters
35. 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
Dependent Selection
Step 1 of a statistical experiment
Probability and statistics
the sample or population mean
36. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
Pairwise independence
The median value
Ratio measurements
That is the median value
37. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.
An estimate of a parameter
The Range
Statistical inference
A Distribution function
38. 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
Sampling Distribution
experimental studies and observational studies.
hypothesis
Cumulative distribution functions
39. Some commonly used symbols for sample statistics
methods of least squares
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
hypotheses
Atomic event
40. 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).
An event
Outlier
Prior probability
descriptive statistics
41. Is that part of a population which is actually observed.
inferential statistics
A sample
Sampling Distribution
variance of X
42. Rejecting a true null hypothesis.
Step 1 of a statistical experiment
Block
Valid measure
Type 1 Error
43. Of a group of numbers is the center point of all those number values.
That value is the median value
The average - or arithmetic mean
the population mean
Ordinal measurements
44. 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
Greek letters
Independence or Statistical independence
The sample space
Confounded variables
45. Statistics involve methods of using information from a sample to draw conclusions regarding the population.
Statistical adjustment
Inferential
s-algebras
Interval measurements
46. Have meaningful distances between measurements defined - but the zero value is arbitrary (as in the case with longitude and temperature measurements in Celsius or Fahrenheit)
Average and arithmetic mean
Interval measurements
Type I errors & Type II errors
Kurtosis
47. 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.
Standard error
Residuals
Independent Selection
categorical variables
48. A numerical measure that describes an aspect of a population.
Descriptive
Parameter
Sampling Distribution
Pairwise independence
49. (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
The Expected value
nominal - ordinal - interval - and ratio
Nominal measurements
Independent Selection
50. Are written in corresponding lower case letters. For example x1 - x2 - ... - xn could be a sample corresponding to the random variable X.
Valid measure
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Particular realizations of a random variable
Pairwise independence