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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. (or multivariate random variable) is a vector whose components are random variables on the same probability space.
Ordinal measurements
Individual
A Random vector
Probability and statistics
2. When info. in a contingency table is re-organized into more or less categories - relationships seen can change or reverse.
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3. 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 Expected value
Interval measurements
Credence
Kurtosis
4. Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically - sometimes they are grouped together as
Correlation
Alpha value (Level of Significance)
Joint probability
categorical variables
5. Many statistical methods seek to minimize the mean-squared error - and these are called
Step 1 of a statistical experiment
Law of Large Numbers
Correlation coefficient
methods of least squares
6. A list of individuals from which the sample is actually selected.
variance of X
A statistic
the population cumulants
Sampling frame
7. Where the null hypothesis is falsely rejected giving a 'false positive'.
Type I errors
Type I errors & Type II errors
nominal - ordinal - interval - and ratio
Experimental and observational studies
8. Data are gathered and correlations between predictors and response are investigated.
Lurking variable
categorical variables
Trend
observational study
9. Is inference about a population from a random sample drawn from it or - more generally - about a random process from its observed behavior during a finite period of time.
Statistical inference
Statistical adjustment
A random variable
Binary data
10. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.
the sample or population mean
Quantitative variable
Descriptive
Sample space
11. A numerical measure that assesses the strength of a linear relationship between two variables.
Average and arithmetic mean
The Range
Correlation coefficient
expected value of X
12. Performing the experiment following the experimental protocol and analyzing the data following the experimental protocol. 4. Further examining the data set in secondary analyses - to suggest new hypotheses for future study. 5. Documenting and present
That is the median value
Step 3 of a statistical experiment
The Expected value
Qualitative variable
13. A collection of events is mutually independent if for any subset of the collection - the joint probability of all events occurring is equal to the product of the joint probabilities of the individual events. Think of the result of a series of coin-fl
Block
A Random vector
Mutual independence
Bias
14. Is the most commonly used measure of statistical dispersion. It is the square root of the variance - and is generally written s (sigma).
A Random vector
The standard deviation
That is the median value
Seasonal effect
15. E[X] :
Confounded variables
The Covariance between two random variables X and Y - with expected values E(X) =
f(z) - and its cdf by F(z).
expected value of X
16. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
Placebo effect
Correlation
Joint distribution
Law of Large Numbers
17. 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
Mutual independence
Beta value
Type I errors & Type II errors
18. Used to reduce bias - this measure weights the more relevant information higher than less relevant info.
Statistical adjustment
Joint distribution
Inferential statistics
Variable
19. The probability of correctly detecting a false null hypothesis.
Power of a test
Trend
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Ratio measurements
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.
Count data
Step 1 of a statistical experiment
A likelihood function
Dependent Selection
21. S^2
A Distribution function
f(z) - and its cdf by F(z).
the population variance
Descriptive
22. (e.g. ? - b) are commonly used to denote unknown parameters (population parameters).
Greek letters
A sampling distribution
Step 2 of a statistical experiment
Individual
23. The collection of all possible outcomes in an experiment.
Descriptive statistics
Sample space
the population mean
the population correlation
24. Given two jointly distributed random variables X and Y - the conditional probability distribution of Y given X (written 'Y | X') is the probability distribution of Y when X is known to be a particular value.
Marginal distribution
The average - or arithmetic mean
the sample or population mean
Conditional distribution
25. Consists of a number of independent trials repeated under identical conditions. On each trial - there are two possible outcomes.
Treatment
Binomial experiment
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Joint distribution
26. Any specific experimental condition applied to the subjects
Mutual independence
covariance of X and Y
descriptive statistics
Treatment
27. The result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data
Posterior probability
Parameter - or 'statistical parameter'
Qualitative variable
f(z) - and its cdf by F(z).
28. 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
Kurtosis
methods of least squares
Probability
Parameter
29. 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
Step 2 of a statistical experiment
Average and arithmetic mean
The Expected value
Parameter
30. Have imprecise differences between consecutive values - but have a meaningful order to those values
Posterior probability
Ordinal measurements
A data point
Type I errors
31. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
Confounded variables
Type II errors
nominal - ordinal - interval - and ratio
A likelihood function
32. (pdfs) and probability mass functions are denoted by lower case letters - e.g. f(x).
Law of Large Numbers
Probability density functions
Seasonal effect
A population or statistical population
33. A measure that is relevant or appropriate as a representation of that property.
Valid measure
Descriptive
The Covariance between two random variables X and Y - with expected values E(X) =
Step 1 of a statistical experiment
34. Failing to reject a false null hypothesis.
Type 2 Error
A sample
Confounded variables
Sampling
35. Var[X] :
Independence or Statistical independence
Observational study
Marginal probability
variance of X
36. 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.
The variance of a random variable
Variability
categorical variables
Marginal probability
37. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
hypotheses
Pairwise independence
Outlier
f(z) - and its cdf by F(z).
38. ?
A data point
the population correlation
Probability density
The standard deviation
39. Statistics involve methods of using information from a sample to draw conclusions regarding the population.
the population mean
Seasonal effect
Inferential
Cumulative distribution functions
40. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
Block
Posterior probability
Null hypothesis
Sampling Distribution
41. 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.
Posterior probability
Statistical adjustment
Statistics
An event
42. 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 estimate of a parameter
the sample or population mean
Parameter - or 'statistical parameter'
The median value
43. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
An Elementary event
Mutual independence
Prior probability
A sample
44. 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
An experimental study
Average and arithmetic mean
Skewness
Step 1 of a statistical experiment
45. 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
Count data
A random variable
Ratio measurements
Inferential statistics
46. A subjective estimate of probability.
Kurtosis
A statistic
Correlation
Credence
47. 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.
Probability density
Divide the sum by the number of values.
Lurking variable
The median value
48. Is a parameter that indexes a family of probability distributions.
Kurtosis
A Statistical parameter
Bias
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
49. (also called statistical variability) is a measure of how diverse some data is. It can be expressed by the variance or the standard deviation.
Statistical dispersion
Simpson's Paradox
A probability space
Prior probability
50. Occurs when a subject receives no treatment - but (incorrectly) believes he or she is in fact receiving treatment and responds favorably.
An estimate of a parameter
An Elementary event
A Distribution function
Placebo effect