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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. Cov[X - Y] :
covariance of X and Y
inferential statistics
Power of a test
Type II 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.
Statistic
A Statistical parameter
the population mean
Estimator
3. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
Pairwise independence
expected value of X
Residuals
Credence
4. Failing to reject a false null hypothesis.
A Distribution function
Parameter - or 'statistical parameter'
Reliable measure
Type 2 Error
5. (also called statistical variability) is a measure of how diverse some data is. It can be expressed by the variance or the standard deviation.
Type II errors
Individual
The standard deviation
Statistical dispersion
6. A variable describes an individual by placing the individual into a category or a group.
A data point
Qualitative variable
Mutual independence
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
7. Is a parameter that indexes a family of probability distributions.
Binomial experiment
A Statistical parameter
Ordinal measurements
A sampling distribution
8. The probability of correctly detecting a false null hypothesis.
Sampling frame
Power of a test
covariance of X and Y
The Expected value
9. A consistent - repeated deviation of the sample statistic from the population parameter in the same direction when many samples are taken.
A Statistical parameter
An experimental study
Bias
Type II errors
10. Some commonly used symbols for population parameters
A probability density function
Joint distribution
Qualitative variable
the population mean
11. Is the most commonly used measure of statistical dispersion. It is the square root of the variance - and is generally written s (sigma).
Average and arithmetic mean
The standard deviation
Sampling
Conditional probability
12. A list of individuals from which the sample is actually selected.
The Range
Ordinal measurements
A Distribution function
Sampling frame
13. A data value that falls outside the overall pattern of the graph.
Statistic
That is the median value
A statistic
Outlier
14. 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.
Standard error
Lurking variable
Reliable measure
Seasonal effect
15. 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.
inferential statistics
Bias
A probability distribution
Reliable measure
16. 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
Parameter - or 'statistical parameter'
Step 2 of a statistical experiment
A data point
A statistic
17. Occurs when a subject receives no treatment - but (incorrectly) believes he or she is in fact receiving treatment and responds favorably.
A data point
Placebo effect
The Expected value
Average and arithmetic mean
18. Var[X] :
Bias
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Conditional distribution
variance of X
19. ?r
The Covariance between two random variables X and Y - with expected values E(X) =
Variability
A Random vector
the population cumulants
20. There are two major types of causal statistical studies: In both types of studies - the effect of differences of an independent variable (or variables) on the behavior of the dependent variable are observed. The difference between the two types lies
A probability distribution
categorical variables
experimental studies and observational studies.
The Mean of a random variable
21. The standard deviation of a sampling distribution.
Parameter - or 'statistical parameter'
Particular realizations of a random variable
Standard error
An event
22. Is a sample space over which a probability measure has been defined.
hypotheses
Pairwise independence
A probability space
Treatment
23. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
A likelihood function
Type 2 Error
P-value
Divide the sum by the number of values.
24. Is a measure of its statistical dispersion - indicating how far from the expected value its values typically are. The variance of random variable X is typically designated as - - or simply s2.
Type I errors & Type II errors
Bias
The variance of a random variable
Treatment
25. Many statistical methods seek to minimize the mean-squared error - and these are called
Probability density
A probability space
A population or statistical population
methods of least squares
26. Data are gathered and correlations between predictors and response are investigated.
observational study
Statistical dispersion
Binomial experiment
Binary data
27. A group of individuals sharing some common features that might affect the treatment.
Block
Conditional probability
Posterior probability
Correlation
28. A numerical measure that describes an aspect of a sample.
Statistic
A data set
applied statistics
The average - or arithmetic mean
29. When there is an even number of values...
The sample space
Experimental and observational studies
Sample space
That is the median value
30. 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
Inferential statistics
Ratio measurements
A Probability measure
The Range
31. Is the result of applying a statistical algorithm to a data set. It can also be described as an observable random variable.
A Statistical parameter
A Random vector
applied statistics
A statistic
32. 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
Null hypothesis
Interval measurements
Sample space
Probability density
33. To find the average - or arithmetic mean - of a set of numbers:
Law of Large Numbers
the population correlation
Correlation coefficient
Divide the sum by the number of values.
34. When info. in a contingency table is re-organized into more or less categories - relationships seen can change or reverse.
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35. Is data that can take only two values - usually represented by 0 and 1.
Binary data
Kurtosis
Random variables
s-algebras
36. 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
inferential statistics
Descriptive statistics
Sampling Distribution
A data point
37. Is that part of a population which is actually observed.
Probability density
categorical variables
A sample
Sampling Distribution
38. Is a sample and the associated data points.
Descriptive
Independent Selection
A data set
Statistical adjustment
39. A measurement such that the random error is small
Reliable measure
Variable
Qualitative variable
Type 1 Error
40. Given two random variables X and Y - the joint distribution of X and Y is the probability distribution of X and Y together.
Sample space
Type 1 Error
Joint distribution
Parameter - or 'statistical parameter'
41. 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
Descriptive statistics
Coefficient of determination
Valid measure
The sample space
42. 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 sample space
Independence or Statistical independence
Nominal measurements
Simpson's Paradox
43. Statistical methods can be used for summarizing or describing a collection of data; this is called
Statistic
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
descriptive statistics
Independence or Statistical independence
44. 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.
That value is the median value
Statistical dispersion
Type I errors
The median value
45. 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.
A population or statistical population
Divide the sum by the number of values.
A Distribution function
A random variable
46. Gives the probability of events in a probability space.
Qualitative variable
A Probability measure
A random variable
Type II errors
47. Consists of a number of independent trials repeated under identical conditions. On each trial - there are two possible outcomes.
Probability density functions
A likelihood function
The Covariance between two random variables X and Y - with expected values E(X) =
Binomial experiment
48. 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.
Particular realizations of a random variable
Conditional probability
That value is the median value
Simple random sample
49. 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
An Elementary event
Statistical inference
Probability density functions
50. 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
covariance of X and Y
hypothesis
Binary data
The Expected value
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