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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.
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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. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
Binomial experiment
A probability density function
Divide the sum by the number of values.
nominal - ordinal - interval - and ratio
2. Cov[X - Y] :
Binomial experiment
covariance of X and Y
Random variables
Probability and statistics
3. ?r
Skewness
Ordinal measurements
Statistical adjustment
the population cumulants
4. A scale that represents an ordinal scale such as looks on a scale from 1 to 10.
Alpha value (Level of Significance)
Likert scale
Correlation
Variable
5. A data value that falls outside the overall pattern of the graph.
covariance of X and Y
Outlier
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Correlation coefficient
6. 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.
Correlation
A Distribution function
A Probability measure
Kurtosis
7. Where the null hypothesis fails to be rejected and an actual difference between populations is missed giving a 'false negative'.
Type II errors
Qualitative variable
Probability and statistics
P-value
8. Error also refers to the extent to which individual observations in a sample differ from a central value - such as
the sample or population mean
Confounded variables
A data point
Simpson's Paradox
9. Where the null hypothesis is falsely rejected giving a 'false positive'.
A data point
A probability density function
Type I errors
Type I errors & Type II errors
10. Is defined as the expected value of random variable (X -
Standard error
The Covariance between two random variables X and Y - with expected values E(X) =
The Mean of a random variable
Pairwise independence
11. 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
Inferential statistics
A random variable
Beta value
Power of a test
12. 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)
Bias
the population variance
Interval measurements
descriptive statistics
13. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
Bias
The Mean of a random variable
P-value
variance of X
14. Many statistical methods seek to minimize the mean-squared error - and these are called
A statistic
methods of least squares
descriptive statistics
The variance of a random variable
15. A measurement such that the random error is small
Reliable measure
Step 1 of a statistical experiment
Probability density functions
Qualitative variable
16. Describes a characteristic of an individual to be measured or observed.
Probability density functions
Variable
Experimental and observational studies
The Range
17. Are usually written with upper case calligraphic (e.g. F for the set of sets on which we define the probability P)
the population correlation
s-algebras
The Range
Cumulative distribution functions
18. Have no meaningful rank order among values.
The average - or arithmetic mean
methods of least squares
Nominal measurements
hypothesis
19. Is the probability of some event A - assuming event B. Conditional probability is written P(A|B) - and is read 'the probability of A - given B'
A data point
The Covariance between two random variables X and Y - with expected values E(X) =
Conditional probability
An experimental study
20. The result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data
Posterior probability
Average and arithmetic mean
An experimental study
the population variance
21. Used to reduce bias - this measure weights the more relevant information higher than less relevant info.
Type II errors
Mutual independence
Confounded variables
Statistical adjustment
22. 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.
Independent Selection
Parameter - or 'statistical parameter'
A population or statistical population
Lurking variable
23. (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 Covariance between two random variables X and Y - with expected values E(X) =
Sampling
Variable
An Elementary event
24. 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.
Treatment
Skewness
Marginal distribution
A sampling distribution
25. Failing to reject a false null hypothesis.
Type II errors
the population mean
Sampling
Type 2 Error
26. Is the length of the smallest interval which contains all the data.
Variable
The Range
Step 2 of a statistical experiment
Probability
27. 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
Treatment
Marginal probability
Confounded variables
Step 2 of a statistical experiment
28. Statistics involve methods of using information from a sample to draw conclusions regarding the population.
Inferential
Parameter
variance of X
Step 2 of a statistical experiment
29. 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.
That is the median value
Independent Selection
Correlation coefficient
The Mean of a random variable
30. ?
A probability distribution
Coefficient of determination
Standard error
the population correlation
31. 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.
That value is the median value
Null hypothesis
Coefficient of determination
Simpson's Paradox
32. (pdfs) and probability mass functions are denoted by lower case letters - e.g. f(x).
The sample space
Probability density functions
Type I errors
The average - or arithmetic mean
33. 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).
Joint probability
Law of Parsimony
methods of least squares
Binary data
34. A numerical measure that describes an aspect of a sample.
Lurking variable
descriptive statistics
An Elementary event
Statistic
35. 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
nominal - ordinal - interval - and ratio
Ratio measurements
Valid measure
The standard deviation
36. Involves taking measurements of the system under study - manipulating the system - and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements.
Quantitative variable
Bias
An experimental study
experimental studies and observational studies.
37. A numerical measure that assesses the strength of a linear relationship between two variables.
categorical variables
Parameter - or 'statistical parameter'
Correlation coefficient
Sampling frame
38. 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
Confounded variables
A Statistical parameter
The sample space
inferential statistics
39. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
Probability density
Observational study
Reliable measure
Prior probability
40. Statistical methods can be used for summarizing or describing a collection of data; this is called
Atomic event
Posterior probability
A probability space
descriptive statistics
41. A common goal for a statistical research project is to investigate causality - and in particular to draw a conclusion on the effect of changes in the values of predictors or independent variables on dependent variables or response.
Experimental and observational studies
Dependent Selection
Statistical dispersion
An experimental study
42. A numerical measure that describes an aspect of a population.
Kurtosis
Descriptive
Parameter
Correlation coefficient
43. E[X] :
expected value of X
Individual
An Elementary event
Variable
44. 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 probability distribution
expected value of X
The average - or arithmetic mean
Probability
45. (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
Seasonal effect
A likelihood function
A sampling distribution
Posterior probability
46. 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
Statistical inference
Power of a test
Step 3 of a statistical experiment
Null hypothesis
47. Gives the probability distribution for a continuous random variable.
Parameter
A probability density function
An Elementary event
Type I errors & Type II errors
48. Describes the spread in the values of the sample statistic when many samples are taken.
Binomial experiment
Variability
Simulation
Valid measure
49. 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.
The standard deviation
A sample
Statistics
Conditional probability
50. Is the probability distribution - under repeated sampling of the population - of a given statistic.
Step 1 of a statistical experiment
A sampling distribution
the population mean
An Elementary event
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