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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. Working from a null hypothesis two basic forms of error are recognized:
descriptive statistics
Binary data
Statistical adjustment
Type I errors & Type II errors
2. Is defined as the expected value of random variable (X -
Block
Experimental and observational studies
Confounded variables
The Covariance between two random variables X and Y - with expected values E(X) =
3. 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.
Statistics
A Random vector
Law of Parsimony
Statistical inference
4. Is the most commonly used measure of statistical dispersion. It is the square root of the variance - and is generally written s (sigma).
the sample or population mean
Simulation
The standard deviation
Step 2 of a statistical experiment
5. ?
Beta value
Treatment
Simulation
the population correlation
6. (or multivariate random variable) is a vector whose components are random variables on the same probability space.
Confounded variables
P-value
Correlation
A Random vector
7. The probability of correctly detecting a false null hypothesis.
Statistics
Power of a test
Statistical inference
Count data
8. 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.
Estimator
A Probability measure
Standard error
Lurking variable
9. Long-term upward or downward movement over time.
Nominal measurements
Skewness
Simulation
Trend
10. Are written in corresponding lower case letters. For example x1 - x2 - ... - xn could be a sample corresponding to the random variable X.
Correlation coefficient
Particular realizations of a random variable
Ratio measurements
Variable
11. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
Sampling Distribution
Variability
A probability space
Outlier
12. Statistics involve methods of using information from a sample to draw conclusions regarding the population.
Inferential
Residuals
descriptive statistics
Trend
13. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
Valid measure
Statistical dispersion
Divide the sum by the number of values.
Prior probability
14. 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 estimate of a parameter
A Probability measure
Conditional distribution
Step 1 of a statistical experiment
15. A measurement such that the random error is small
Simulation
Reliable measure
A Statistical parameter
Beta value
16. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
nominal - ordinal - interval - and ratio
Conditional distribution
Valid measure
An estimate of a parameter
17. 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).
Conditional probability
quantitative variables
Joint probability
the population mean
18. (pdfs) and probability mass functions are denoted by lower case letters - e.g. f(x).
The sample space
Beta value
Probability density functions
The standard deviation
19. 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
Ratio measurements
descriptive statistics
Step 2 of a statistical experiment
Lurking variable
20. A numerical measure that describes an aspect of a population.
Step 1 of a statistical experiment
A data set
Parameter
Marginal probability
21. Have imprecise differences between consecutive values - but have a meaningful order to those values
Prior probability
Variable
Ordinal measurements
Statistics
22. In number theory - scatter plots of data generated by a distribution function may be transformed with familiar tools used in statistics to reveal underlying patterns - which may then lead to
Divide the sum by the number of values.
hypotheses
Independent Selection
Law of Parsimony
23. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.
Average and arithmetic mean
Outlier
Divide the sum by the number of values.
An estimate of a parameter
24. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.
Descriptive
Placebo effect
Type II errors
covariance of X and Y
25. Where the null hypothesis fails to be rejected and an actual difference between populations is missed giving a 'false negative'.
applied statistics
Type II errors
A population or statistical population
Valid measure
26. (also called statistical variability) is a measure of how diverse some data is. It can be expressed by the variance or the standard deviation.
Sample space
Conditional probability
Statistical dispersion
Bias
27. A numerical facsimilie or representation of a real-world phenomenon.
An Elementary event
Parameter
Simulation
A random variable
28. A measure that is relevant or appropriate as a representation of that property.
Valid measure
covariance of X and Y
Cumulative distribution functions
Reliable measure
29. S^2
hypothesis
The standard deviation
observational study
the population variance
30. Describes the spread in the values of the sample statistic when many samples are taken.
Dependent Selection
Kurtosis
Variability
A data set
31. 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.
Nominal measurements
Statistical inference
Binomial experiment
Descriptive
32. The result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data
Sample space
Sampling Distribution
Posterior probability
descriptive statistics
33. Some commonly used symbols for sample statistics
the population variance
Residuals
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Variability
34. Ratio and interval measurements which can be either discrete or continuous - due to their numerical nature are grouped together as
A likelihood function
The Expected value
quantitative variables
A sample
35. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
Pairwise independence
hypothesis
Inferential
Coefficient of determination
36. 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
Variable
The average - or arithmetic mean
the population cumulants
37. Is a parameter that indexes a family of probability distributions.
A Statistical parameter
The average - or arithmetic mean
Sampling
Probability
38. Is its expected value. The mean (or sample mean of a data set is just the average value.
The Mean of a random variable
Ordinal measurements
That is the median value
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
39. Are simply two different terms for the same thing. Add the given values
Posterior probability
Average and arithmetic mean
A Statistical parameter
descriptive statistics
40. 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.
A data point
Likert scale
A Distribution function
Independence or Statistical independence
41. Is the result of applying a statistical algorithm to a data set. It can also be described as an observable random variable.
Type II errors
A statistic
The standard deviation
Cumulative distribution functions
42. When info. in a contingency table is re-organized into more or less categories - relationships seen can change or reverse.
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43. Is the probability distribution - under repeated sampling of the population - of a given statistic.
f(z) - and its cdf by F(z).
The Expected value
A sampling distribution
Reliable measure
44. 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.
An experimental study
Sampling
Conditional distribution
Cumulative distribution functions
45. (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.
Simpson's Paradox
An Elementary event
Average and arithmetic mean
Descriptive statistics
46. A variable describes an individual by placing the individual into a category or a group.
the sample or population mean
Qualitative variable
A random variable
Ordinal measurements
47. 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)
Statistic
covariance of X and Y
The Range
Interval measurements
48. 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
Bias
The average - or arithmetic mean
Type I errors & Type II errors
49. Is a sample and the associated data points.
Random variables
Sampling frame
That is the median value
A data set
50. The collection of all possible outcomes in an experiment.
observational study
Sample space
Qualitative variable
Type 1 Error
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