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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. Where the null hypothesis is falsely rejected giving a 'false positive'.
A data set
Residuals
P-value
Type I errors
2. 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.
Estimator
Particular realizations of a random variable
Type I errors & Type II errors
Independence or Statistical independence
3. Many statistical methods seek to minimize the mean-squared error - and these are called
A probability density function
A Statistical parameter
P-value
methods of least squares
4. A scale that represents an ordinal scale such as looks on a scale from 1 to 10.
Simulation
Likert scale
Power of a test
An Elementary event
5. 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
P-value
Lurking variable
Reliable measure
Probability
6. Var[X] :
Probability and statistics
f(z) - and its cdf by F(z).
Interval measurements
variance of X
7. ?
Step 2 of a statistical experiment
Statistical dispersion
Placebo effect
the population correlation
8. Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically - sometimes they are grouped together as
categorical variables
A probability density function
Nominal measurements
The median value
9. Are simply two different terms for the same thing. Add the given values
methods of least squares
Average and arithmetic mean
Probability and statistics
Statistics
10. Is the probability distribution - under repeated sampling of the population - of a given statistic.
the population mean
Step 2 of a statistical experiment
Likert scale
A sampling distribution
11. Is denoted by - pronounced 'x bar'.
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
observational study
Skewness
Correlation coefficient
12. Are usually written in upper case roman letters: X - Y - etc.
Step 3 of a statistical experiment
Greek letters
Random variables
Prior probability
13. 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.
Lurking variable
Probability density functions
Divide the sum by the number of values.
Sampling
14. Failing to reject a false null hypothesis.
hypotheses
observational study
Type 2 Error
Conditional distribution
15. (pdfs) and probability mass functions are denoted by lower case letters - e.g. f(x).
Probability density functions
A Statistical parameter
Reliable measure
methods of least squares
16. Are usually written with upper case calligraphic (e.g. F for the set of sets on which we define the probability P)
Marginal distribution
the sample or population mean
Treatment
s-algebras
17. 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 sample space
Lurking variable
P-value
Observational study
18. A measure that is relevant or appropriate as a representation of that property.
Valid measure
Skewness
Standard error
variance of X
19. 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
Sampling frame
Inferential statistics
Statistic
the population correlation
20. Is the result of applying a statistical algorithm to a data set. It can also be described as an observable random variable.
A Probability measure
Pairwise independence
A statistic
Null hypothesis
21. 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.
An Elementary event
hypothesis
Statistics
Marginal distribution
22. Gives the probability distribution for a continuous random variable.
Outlier
A probability density function
Confounded variables
hypothesis
23. A numerical measure that assesses the strength of a linear relationship between two variables.
Mutual independence
Particular realizations of a random variable
Correlation coefficient
That is the median value
24. Working from a null hypothesis two basic forms of error are recognized:
Quantitative variable
Type I errors & Type II errors
The Range
Atomic event
25. (or just likelihood) is a conditional probability function considered a function of its second argument with its first argument held fixed. For example - imagine pulling a numbered ball with the number k from a bag of n balls - numbered 1 to n. Then
Descriptive statistics
The standard deviation
A likelihood function
Parameter
26. 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.
Standard error
Marginal probability
Type I errors & Type II errors
Beta value
27. A data value that falls outside the overall pattern of the graph.
Outlier
Trend
A data point
The Range
28. Of a group of numbers is the center point of all those number values.
The average - or arithmetic mean
A data point
s-algebras
categorical variables
29. Given two random variables X and Y - the joint distribution of X and Y is the probability distribution of X and Y together.
That is the median value
Joint distribution
Statistical dispersion
Marginal probability
30. In number theory - scatter plots of data generated by a distribution function may be transformed with familiar tools used in statistics to reveal underlying patterns - which may then lead to
s-algebras
Residuals
hypotheses
Descriptive
31. 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.
An experimental study
Mutual independence
The median value
Statistical inference
32. (cdfs) are denoted by upper case letters - e.g. F(x).
Cumulative distribution functions
Parameter - or 'statistical parameter'
Standard error
the population variance
33. 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
A probability density function
Descriptive statistics
Independent Selection
the population variance
34. Have both a meaningful zero value and the distances between different measurements defined; they provide the greatest flexibility in statistical methods that can be used for analyzing the data
Ratio measurements
Observational study
Type 1 Error
A Random vector
35. A list of individuals from which the sample is actually selected.
Sampling frame
Particular realizations of a random variable
Treatment
Placebo effect
36. Is the length of the smallest interval which contains all the data.
Variability
A sampling distribution
Bias
The Range
37. 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).
That is the median value
Skewness
Joint probability
Ordinal measurements
38. 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 population mean
Independence or Statistical independence
Parameter - or 'statistical parameter'
Kurtosis
39. Is data that can take only two values - usually represented by 0 and 1.
Estimator
The Mean of a random variable
Binary data
Statistical dispersion
40. 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
The Mean of a random variable
inferential statistics
the population correlation
Descriptive
41. 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.
42. (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.
Particular realizations of a random variable
That is the median value
An Elementary event
categorical variables
43. (or multivariate random variable) is a vector whose components are random variables on the same probability space.
Probability density functions
A Random vector
Sampling frame
the sample or population mean
44. Interpretation of statistical information in that the assumption is that whatever is proposed as a cause has no effect on the variable being measured can often involve the development of a
A probability space
Qualitative variable
Null hypothesis
A probability density function
45. ?r
the population mean
Step 3 of a statistical experiment
Probability density functions
the population cumulants
46. Two variables such that their effects on the response variable cannot be distinguished from each other.
A likelihood function
Statistics
The Expected value
Confounded variables
47. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
the population cumulants
the population variance
Pairwise independence
applied statistics
48. 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.
Lurking variable
Law of Parsimony
A Distribution function
That value is the median value
49. Any specific experimental condition applied to the subjects
Marginal distribution
Statistic
Skewness
Treatment
50. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
Interval measurements
Prior probability
Correlation coefficient
A Statistical parameter