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Test your basic knowledge |
CLEP General Mathematics: Probability And Statistics
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Subjects
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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. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
Probability density functions
hypothesis
nominal - ordinal - interval - and ratio
expected value of X
2. 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.
Mutual independence
A data set
Conditional distribution
A Distribution function
3. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
The Expected value
Inferential
Prior probability
Simple random sample
4. 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.
Mutual independence
The variance of a random variable
Marginal probability
Seasonal effect
5. Occurs when a subject receives no treatment - but (incorrectly) believes he or she is in fact receiving treatment and responds favorably.
Divide the sum by the number of values.
Seasonal effect
An event
Placebo effect
6. ?r
the population cumulants
Binomial experiment
Sampling Distribution
A data point
7. 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
hypothesis
applied statistics
Reliable measure
Mutual independence
8. (or multivariate random variable) is a vector whose components are random variables on the same probability space.
Bias
A Random vector
Simpson's Paradox
The Mean of a random variable
9. Any specific experimental condition applied to the subjects
the population mean
Simpson's Paradox
Treatment
Simple random sample
10. Gives the probability of events in a probability space.
Binomial experiment
Bias
Divide the sum by the number of values.
A Probability measure
11. In particular - the pdf of the standard normal distribution is denoted by
Statistical adjustment
Variable
f(z) - and its cdf by F(z).
Outlier
12. 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.
Probability and statistics
Sampling Distribution
the sample or population mean
Marginal distribution
13. Is one that explores the correlation between smoking and lung cancer. This type of study typically uses a survey to collect observations about the area of interest and then performs statistical analysis. In this case - the researchers would collect o
Statistical adjustment
Observational study
The Range
Binomial experiment
14. 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.
categorical variables
the population mean
Experimental and observational studies
A probability distribution
15. A group of individuals sharing some common features that might affect the treatment.
Block
A random variable
Trend
Likert scale
16. 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.
Correlation coefficient
Ratio measurements
Type 2 Error
A population or statistical population
17. Data are gathered and correlations between predictors and response are investigated.
Divide the sum by the number of values.
the population cumulants
observational study
Statistic
18. A numerical measure that describes an aspect of a population.
Parameter - or 'statistical parameter'
Cumulative distribution functions
Parameter
Bias
19. 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).
A probability density function
Seasonal effect
Joint probability
Residuals
20. 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.
Coefficient of determination
Valid measure
A Distribution function
Simple random sample
21. Is defined as the expected value of random variable (X -
The sample space
covariance of X and Y
That value is the median value
The Covariance between two random variables X and Y - with expected values E(X) =
22. S^2
Correlation coefficient
the population variance
nominal - ordinal - interval - and ratio
A likelihood function
23. Is denoted by - pronounced 'x bar'.
Variability
covariance of X and Y
Estimator
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
24. 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
Marginal probability
Standard error
Statistical adjustment
25. Failing to reject a false null hypothesis.
Posterior probability
covariance of X and Y
the population mean
Type 2 Error
26. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
A likelihood function
Law of Large Numbers
A population or statistical population
Variable
27. 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.
Conditional distribution
The sample space
The variance of a random variable
An experimental study
28. A data value that falls outside the overall pattern of the graph.
A sampling distribution
Outlier
Inferential
Ratio measurements
29. A measurement such that the random error is small
Reliable measure
covariance of X and Y
the population mean
The Expected value
30. 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)
Interval measurements
A Distribution function
categorical variables
P-value
31. Where the null hypothesis is falsely rejected giving a 'false positive'.
A Random vector
Quantitative variable
Type I errors
Coefficient of determination
32. When info. in a contingency table is re-organized into more or less categories - relationships seen can change or reverse.
33. Have imprecise differences between consecutive values - but have a meaningful order to those values
observational study
Count data
Ordinal measurements
A Statistical parameter
34. Statistical methods can be used for summarizing or describing a collection of data; this is called
Correlation coefficient
Simpson's Paradox
descriptive statistics
Type 1 Error
35. 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
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
applied statistics
Nominal measurements
Null hypothesis
36. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively
Residuals
The Mean of a random variable
A random variable
An estimate of a parameter
37. Error also refers to the extent to which individual observations in a sample differ from a central value - such as
Residuals
The Range
the sample or population mean
Probability density
38. The objects described by a set of data: person (animal) - place - and - thing. (SUBJECTS)
A data point
Skewness
Individual
The Mean of a random variable
39. ?
Treatment
the population correlation
Mutual independence
A Distribution function
40. Describes a characteristic of an individual to be measured or observed.
Power of a test
Atomic event
Variable
Correlation coefficient
41. Given two random variables X and Y - the joint distribution of X and Y is the probability distribution of X and Y together.
Joint distribution
the population cumulants
That is the median value
A Statistical parameter
42. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
Sampling Distribution
Independence or Statistical independence
Statistical adjustment
Step 1 of a statistical experiment
43. 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
Mutual independence
Bias
Conditional probability
44. A variable describes an individual by placing the individual into a category or a group.
Qualitative variable
Simulation
Standard error
Alpha value (Level of Significance)
45. Many statistical methods seek to minimize the mean-squared error - and these are called
s-algebras
Lurking variable
methods of least squares
Simulation
46. 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
the population mean
Independent Selection
Simulation
Inferential statistics
47. 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
Correlation coefficient
Mutual independence
experimental studies and observational studies.
Type 2 Error
48. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.
An experimental study
Marginal distribution
Descriptive
Bias
49. 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.
Independent Selection
Simulation
Binomial experiment
Joint probability
50. 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).
Conditional probability
nominal - ordinal - interval - and ratio
An event
Experimental and observational studies