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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.
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. Also called correlation coefficient - is a numeric measure of the strength of linear relationship between two random variables (one can use it to quantify - for example - how shoe size and height are correlated in the population). An example is the P
Correlation
Dependent Selection
expected value of X
Kurtosis
2. 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
Null hypothesis
Interval measurements
The sample space
Count data
3. Summarize the population data by describing what was observed in the sample numerically or graphically. Numerical descriptors include mean and standard deviation for continuous data types (like heights or weights) - while frequency and percentage are
variance of X
the population mean
Descriptive statistics
Outlier
4. Is data arising from counting that can take only non-negative integer values.
Statistics
A likelihood function
Seasonal effect
Count data
5. 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 population mean
Kurtosis
inferential statistics
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
6. The result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data
Posterior probability
Parameter
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
A population or statistical population
7. 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
Conditional probability
Experimental and observational studies
Null hypothesis
8. Gives the probability of events in a probability space.
A sampling distribution
Step 1 of a statistical experiment
Lurking variable
A Probability measure
9. Are usually written in upper case roman letters: X - Y - etc.
the population cumulants
the population variance
The Range
Random variables
10. 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.
Qualitative variable
Estimator
Probability
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
11. 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
Residuals
Individual
A data point
12. Var[X] :
variance of X
Statistical dispersion
Treatment
A data set
13. Some commonly used symbols for population parameters
Binary data
descriptive statistics
the population mean
Type 1 Error
14. Failing to reject a false null hypothesis.
Beta value
Type 2 Error
An experimental study
The median value
15. The probability of correctly detecting a false null hypothesis.
Simple random sample
Statistical inference
Power of a test
experimental studies and observational studies.
16. Is defined as the expected value of random variable (X -
f(z) - and its cdf by F(z).
the population mean
The Covariance between two random variables X and Y - with expected values E(X) =
Treatment
17. (cdfs) are denoted by upper case letters - e.g. F(x).
Particular realizations of a random variable
Cumulative distribution functions
An experimental study
Skewness
18. Are usually written with upper case calligraphic (e.g. F for the set of sets on which we define the probability P)
s-algebras
Likert scale
Probability and statistics
Confounded variables
19. Probability of rejecting a true null hypothesis.
Alpha value (Level of Significance)
Descriptive
methods of least squares
f(z) - and its cdf by F(z).
20. 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.
A data point
That value is the median value
Count data
Placebo effect
21. Is a function that gives the probability of all elements in a given space: see List of probability distributions
A probability density function
A probability distribution
expected value of X
the population mean
22. Have no meaningful rank order among values.
covariance of X and Y
The variance of a random variable
Nominal measurements
The Expected value
23. The standard deviation of a sampling distribution.
Standard error
Statistical dispersion
the sample or population mean
Ratio measurements
24. Is the set of possible outcomes of an experiment. For example - the sample space for rolling a six-sided die will be {1 - 2 - 3 - 4 - 5 - 6}.
Step 1 of a statistical experiment
hypothesis
The sample space
Seasonal effect
25. 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.
Conditional distribution
Marginal distribution
Independent Selection
The sample space
26. (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
A likelihood function
Statistical adjustment
That is the median value
A statistic
27. ?r
A probability space
the population cumulants
A sampling distribution
Individual
28. S^2
Joint probability
the population variance
Statistical adjustment
hypotheses
29. Used to reduce bias - this measure weights the more relevant information higher than less relevant info.
That is the median value
Sampling frame
observational study
Statistical adjustment
30. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
Null hypothesis
P-value
Statistical adjustment
covariance of X and Y
31. 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
Ratio measurements
Inferential statistics
A Random vector
Conditional distribution
32. 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.
That value is the median value
Sampling
the population variance
Prior probability
33. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
A sampling distribution
nominal - ordinal - interval - and ratio
That is the median value
Confounded variables
34. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
The variance of a random variable
Sampling Distribution
Estimator
Cumulative distribution functions
35. Describes the spread in the values of the sample statistic when many samples are taken.
Inferential
Kurtosis
Treatment
Variability
36. A subjective estimate of probability.
Correlation
observational study
Credence
Inferential statistics
37. Are written in corresponding lower case letters. For example x1 - x2 - ... - xn could be a sample corresponding to the random variable X.
Atomic event
Posterior probability
Particular realizations of a random variable
Independent Selection
38. A numerical measure that describes an aspect of a sample.
Statistic
A data set
A data point
The median value
39.
Simple random sample
methods of least squares
Lurking variable
the population mean
40. Is the length of the smallest interval which contains all the data.
Probability
Step 1 of a statistical experiment
The median value
The Range
41. When you have two or more competing models - choose the simpler of the two models.
Law of Parsimony
Conditional distribution
Credence
the population variance
42. 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
Estimator
expected value of X
Probability density
43. Is data that can take only two values - usually represented by 0 and 1.
A sample
A Distribution function
Binary data
Joint probability
44. A variable describes an individual by placing the individual into a category or a group.
A data point
Parameter
the sample or population mean
Qualitative variable
45. Cov[X - Y] :
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
covariance of X and Y
A Random vector
Interval measurements
46. Is a measure of the asymmetry of the probability distribution of a real-valued random variable. Roughly speaking - a distribution has positive skew (right-skewed) if the higher tail is longer and negative skew (left-skewed) if the lower tail is longe
A data point
Skewness
s-algebras
Probability
47. Are two related but separate academic disciplines. Statistical analysis often uses probability distributions - and the two topics are often studied together. However - probability theory contains much that is of mostly of mathematical interest and no
quantitative variables
Probability and statistics
An Elementary event
the population correlation
48. 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.
An experimental study
A Probability measure
Lurking variable
nominal - ordinal - interval - and ratio
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.
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
An estimate of a parameter
Statistical dispersion
Skewness
50. Long-term upward or downward movement over time.
Qualitative variable
The Expected value
The Covariance between two random variables X and Y - with expected values E(X) =
Trend
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