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Test your basic knowledge |
CLEP General Mathematics: Probability And Statistics
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Study First
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. Are usually written in upper case roman letters: X - Y - etc.
Step 1 of a statistical experiment
Inferential statistics
Random variables
Trend
2. A measure that is relevant or appropriate as a representation of that property.
Valid measure
A probability distribution
Cumulative distribution functions
Confounded variables
3. The objects described by a set of data: person (animal) - place - and - thing. (SUBJECTS)
A probability space
Ratio measurements
Estimator
Individual
4. To find the average - or arithmetic mean - of a set of numbers:
Divide the sum by the number of values.
Trend
Bias
Probability
5. Probability of accepting a false null hypothesis.
Divide the sum by the number of values.
Beta value
Sampling frame
Mutual independence
6. 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
hypothesis
Sampling frame
Skewness
Step 2 of a statistical experiment
7. Is defined as the expected value of random variable (X -
The median value
The Covariance between two random variables X and Y - with expected values E(X) =
hypotheses
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
8. 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.
Binary data
Bias
hypotheses
Average and arithmetic mean
9. When you have two or more competing models - choose the simpler of the two models.
The variance of a random variable
Law of Parsimony
Valid measure
Individual
10. 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
categorical variables
Probability
Type 1 Error
Correlation
11. Can be - for example - the possible outcomes of a dice roll (but it is not assigned a value). The distribution function of a random variable gives the probability of different results. We can also derive the mean and variance of a random variable.
A random variable
Descriptive statistics
the population mean
A sampling distribution
12. A measurement such that the random error is small
A probability space
Reliable measure
covariance of X and Y
Trend
13. Statistics involve methods of using information from a sample to draw conclusions regarding the population.
Observational study
inferential statistics
Inferential
An event
14. Given two random variables X and Y - the joint distribution of X and Y is the probability distribution of X and Y together.
Simulation
Joint distribution
Seasonal effect
A Statistical parameter
15. Is a sample space over which a probability measure has been defined.
An estimate of a parameter
Lurking variable
A probability space
Bias
16. (or multivariate random variable) is a vector whose components are random variables on the same probability space.
Type I errors
Outlier
Independent Selection
A Random vector
17. A numerical facsimilie or representation of a real-world phenomenon.
Binary data
Independence or Statistical independence
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Simulation
18. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
Simple random sample
Sampling Distribution
A probability space
hypothesis
19. 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
Placebo effect
Type I errors & Type II errors
A population or statistical population
20. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively
Residuals
Type I errors & Type II errors
Sample space
the population cumulants
21. (or expectation) of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by its payoff ('value'). Thus - it represents the average amount one 'expects' to win per bet if bets with identical odds are re
An Elementary event
A probability density function
The Expected value
Descriptive statistics
22. 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.
A Statistical parameter
A statistic
Conditional probability
That value is the median value
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.
Independence or Statistical independence
A random variable
An Elementary event
An experimental study
24. 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.
observational study
A Distribution function
applied statistics
Sampling Distribution
25. 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.
inferential statistics
the population cumulants
Independent Selection
Valid measure
26. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
Trend
Probability density functions
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
nominal - ordinal - interval - and ratio
27. The standard deviation of a sampling distribution.
the sample or population mean
Standard error
Statistic
Quantitative variable
28. A consistent - repeated deviation of the sample statistic from the population parameter in the same direction when many samples are taken.
Posterior probability
A Random vector
categorical variables
Bias
29. Is a parameter that indexes a family of probability distributions.
A Statistical parameter
Outlier
Conditional probability
Variable
30. Is a sample and the associated data points.
Probability
categorical variables
A data set
s-algebras
31. 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
Type I errors
Step 3 of a statistical experiment
Block
Standard error
32. Where the null hypothesis fails to be rejected and an actual difference between populations is missed giving a 'false negative'.
Type I errors
the sample or population mean
Type II errors
applied statistics
33. When there is an even number of values...
the population mean
Likert scale
Ratio measurements
That is the median value
34. Data are gathered and correlations between predictors and response are investigated.
observational study
the sample or population mean
Inferential
Kurtosis
35. 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
Marginal probability
Random variables
Outlier
36. Cov[X - Y] :
covariance of X and Y
The standard deviation
methods of least squares
Prior probability
37. Consists of a number of independent trials repeated under identical conditions. On each trial - there are two possible outcomes.
Greek letters
descriptive statistics
Estimator
Binomial experiment
38. Describes the spread in the values of the sample statistic when many samples are taken.
Variability
Marginal distribution
Sampling frame
Residuals
39. Where the null hypothesis is falsely rejected giving a 'false positive'.
Beta value
Statistical inference
Type I errors
quantitative variables
40. Is a process of selecting observations to obtain knowledge about a population. There are many methods to choose on which sample to do the observations.
Coefficient of determination
Sampling
Binomial experiment
The average - or arithmetic mean
41. 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'
the population correlation
f(z) - and its cdf by F(z).
hypotheses
Conditional probability
42. Are written in corresponding lower case letters. For example x1 - x2 - ... - xn could be a sample corresponding to the random variable X.
The Mean of a random variable
Particular realizations of a random variable
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Type II errors
43. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
the population cumulants
P-value
covariance of X and Y
Average and arithmetic mean
44. Some commonly used symbols for population parameters
the population mean
Correlation coefficient
Skewness
Marginal distribution
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
Parameter - or 'statistical parameter'
A likelihood function
A data set
categorical variables
46. ?
the population correlation
The sample space
the population mean
Valid measure
47. 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.
48. Another name for elementary event.
Outlier
Joint probability
A probability distribution
Atomic event
49. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.
Quantitative variable
An event
Descriptive
s-algebras
50. 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.
hypotheses
Estimator
Probability and statistics
categorical variables