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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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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. Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically - sometimes they are grouped together as
Probability density functions
the population correlation
The variance of a random variable
categorical variables
2. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
Simpson's Paradox
Sampling Distribution
A likelihood function
Probability and statistics
3. Is a typed measurement - it can be a boolean value - a real number - a vector (in which case it's also called a data vector) - etc.
Variability
A Statistical parameter
Qualitative variable
A data point
4. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.
Descriptive
Count data
Likert scale
Statistics
5. In particular - the pdf of the standard normal distribution is denoted by
A probability density function
f(z) - and its cdf by F(z).
An experimental study
The average - or arithmetic mean
6. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.
An estimate of a parameter
A Statistical parameter
Sampling
inferential statistics
7. Error also refers to the extent to which individual observations in a sample differ from a central value - such as
A sample
The median value
the sample or population mean
Sampling Distribution
8. Is its expected value. The mean (or sample mean of a data set is just the average value.
Residuals
The Mean of a random variable
Descriptive statistics
The variance of a random variable
9. Is data that can take only two values - usually represented by 0 and 1.
Valid measure
Kurtosis
A statistic
Binary data
10. A consistent - repeated deviation of the sample statistic from the population parameter in the same direction when many samples are taken.
Bias
Dependent Selection
Step 2 of a statistical experiment
The Range
11. The standard deviation of a sampling distribution.
expected value of X
Standard error
Law of Large Numbers
Mutual independence
12. Is a function that gives the probability of all elements in a given space: see List of probability distributions
categorical variables
The Mean of a random variable
Credence
A probability distribution
13. 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.
Bias
That is the median value
Standard error
A Distribution function
14. Given two random variables X and Y - the joint distribution of X and Y is the probability distribution of X and Y together.
experimental studies and observational studies.
Dependent Selection
Joint distribution
The Expected value
15. 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'
Seasonal effect
A data point
Step 1 of a statistical experiment
Conditional probability
16. Are simply two different terms for the same thing. Add the given values
Step 1 of a statistical experiment
Individual
A Distribution function
Average and arithmetic mean
17. 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
Valid measure
Mutual independence
A statistic
18. (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
Seasonal effect
Independence or Statistical independence
Likert scale
A likelihood function
19. Is that part of a population which is actually observed.
A sample
A likelihood function
Valid measure
Treatment
20. 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.
Atomic event
Variable
Marginal distribution
Average and arithmetic mean
21. Some commonly used symbols for population parameters
the population mean
the population cumulants
Average and arithmetic mean
A statistic
22. A numerical measure that describes an aspect of a population.
Reliable measure
Parameter
A statistic
Correlation
23. 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.
the sample or population mean
the population mean
The median value
Statistics
24. Long-term upward or downward movement over time.
Step 3 of a statistical experiment
Greek letters
Trend
Bias
25. 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.
the population mean
Treatment
Law of Large Numbers
An experimental study
26. Gives the probability of events in a probability space.
Random variables
An estimate of a parameter
A Probability measure
observational study
27. Probability of rejecting a true null hypothesis.
Joint probability
expected value of X
Alpha value (Level of Significance)
Skewness
28. Used to reduce bias - this measure weights the more relevant information higher than less relevant info.
Reliable measure
A probability space
Statistical adjustment
Simple random sample
29. 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
Power of a test
Independent Selection
The Mean of a random variable
inferential statistics
30. 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.
Sampling
A random variable
A probability space
Coefficient of determination
31. 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.
the population correlation
Probability density functions
Step 2 of a statistical experiment
Dependent Selection
32. The objects described by a set of data: person (animal) - place - and - thing. (SUBJECTS)
Trend
Individual
Probability and statistics
An estimate of a parameter
33. The probability of correctly detecting a false null hypothesis.
Power of a test
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Mutual independence
Dependent Selection
34. Is a parameter that indexes a family of probability distributions.
Alpha value (Level of Significance)
A Statistical parameter
Statistical inference
Statistics
35. 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
Credence
Probability
Type 1 Error
Correlation coefficient
36. Is the length of the smallest interval which contains all the data.
The Range
Binomial experiment
Credence
hypotheses
37. S^2
Joint probability
Marginal probability
the population variance
observational study
38. Some commonly used symbols for sample statistics
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Kurtosis
nominal - ordinal - interval - and ratio
A probability space
39. A variable describes an individual by placing the individual into a category or a group.
Likert scale
Probability
A statistic
Qualitative variable
40. Statistics involve methods of using information from a sample to draw conclusions regarding the population.
Divide the sum by the number of values.
Inferential
Simulation
Skewness
41. 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.
Power of a test
A population or statistical population
Type 2 Error
Sampling
42. Cov[X - Y] :
Marginal probability
covariance of X and Y
Sampling frame
Ratio measurements
43. 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.
Independence or Statistical independence
Count data
Marginal probability
Ratio measurements
44. A scale that represents an ordinal scale such as looks on a scale from 1 to 10.
Reliable measure
Placebo effect
Likert scale
the population cumulants
45. The result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data
Correlation
Posterior probability
hypothesis
Statistic
46. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
Experimental and observational studies
Type I errors
Sampling
P-value
47. A measure that is relevant or appropriate as a representation of that property.
Inferential
Marginal distribution
Law of Parsimony
Valid measure
48. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Experimental and observational studies
A population or statistical population
nominal - ordinal - interval - and ratio
49. Another name for elementary event.
Atomic event
An Elementary event
An experimental study
Correlation
50. Is a sample and the associated data points.
A data set
methods of least squares
Random variables
inferential statistics