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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. 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
Prior probability
A sample
Step 2 of a statistical experiment
the population correlation
2. Two events are independent if the outcome of one does not affect that of the other (for example - getting a 1 on one die roll does not affect the probability of getting a 1 on a second roll). Similarly - when we assert that two random variables are i
Greek letters
Divide the sum by the number of values.
Step 2 of a statistical experiment
Independence or Statistical independence
3. 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
Beta value
Statistical dispersion
A data point
hypothesis
4. 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'
Conditional probability
Alpha value (Level of Significance)
Standard error
The average - or arithmetic mean
5. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
Confounded variables
nominal - ordinal - interval - and ratio
Estimator
Alpha value (Level of Significance)
6. When you have two or more competing models - choose the simpler of the two models.
Reliable measure
Simpson's Paradox
Conditional probability
Law of Parsimony
7. A numerical measure that describes an aspect of a sample.
Statistic
the population mean
Marginal distribution
Standard error
8. 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
the sample or population mean
Skewness
Ordinal measurements
Probability and statistics
9. Are written in corresponding lower case letters. For example x1 - x2 - ... - xn could be a sample corresponding to the random variable X.
the population mean
Particular realizations of a random variable
The average - or arithmetic mean
Correlation coefficient
10. 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.
A population or statistical population
Treatment
Marginal distribution
Null hypothesis
11. Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically - sometimes they are grouped together as
the sample or population mean
categorical variables
methods of least squares
Step 3 of a statistical experiment
12. 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.
13. 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
Marginal probability
Mutual independence
the population mean
Inferential statistics
14. 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.
experimental studies and observational studies.
Binomial experiment
Nominal measurements
Statistical inference
15. 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.
The sample space
f(z) - and its cdf by F(z).
Lurking variable
Observational study
16. 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
Trend
Descriptive statistics
Statistical dispersion
Outlier
17. 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}.
The sample space
Sampling
Interval measurements
Standard error
18. Is the length of the smallest interval which contains all the data.
Conditional distribution
Observational study
The Range
Sample space
19. E[X] :
expected value of X
Outlier
A sample
experimental studies and observational studies.
20. Where the null hypothesis is falsely rejected giving a 'false positive'.
Type I errors
A Statistical parameter
Type I errors & Type II errors
Bias
21. 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.
Probability density functions
Bias
That is the median value
Type I errors & Type II errors
22. (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
Skewness
Step 1 of a statistical experiment
quantitative variables
The Expected value
23. A measure that is relevant or appropriate as a representation of that property.
Qualitative variable
Valid measure
A likelihood function
The variance of a random variable
24. 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.
Greek letters
A data point
Reliable measure
A Random vector
25. (e.g. ? - b) are commonly used to denote unknown parameters (population parameters).
expected value of X
the sample or population mean
Greek letters
Joint probability
26. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
P-value
descriptive statistics
quantitative variables
Coefficient of determination
27. Data are gathered and correlations between predictors and response are investigated.
the population variance
A probability space
observational study
Type I errors & Type II errors
28. (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
Step 2 of a statistical experiment
hypotheses
A likelihood function
Sample space
29. Probability of accepting a false null hypothesis.
An Elementary event
Greek letters
Beta value
observational study
30. The result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data
Sampling
An estimate of a parameter
Posterior probability
Credence
31. A variable describes an individual by placing the individual into a category or a group.
Statistical adjustment
Step 1 of a statistical experiment
Kurtosis
Qualitative variable
32. 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.
Mutual independence
Variable
A random variable
covariance of X and Y
33. 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
Dependent Selection
Reliable measure
A Probability measure
34. Is its expected value. The mean (or sample mean of a data set is just the average value.
A probability space
The Mean of a random variable
Confounded variables
Likert scale
35. Descriptive statistics and inferential statistics (a.k.a. - predictive statistics) together comprise
Estimator
applied statistics
Correlation coefficient
Step 3 of a statistical experiment
36. Error also refers to the extent to which individual observations in a sample differ from a central value - such as
Credence
Standard error
P-value
the sample or population mean
37. Describes the spread in the values of the sample statistic when many samples are taken.
Seasonal effect
Variability
Statistical dispersion
A population or statistical population
38. 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.
Null hypothesis
Estimator
observational study
Inferential
39. A numerical measure that describes an aspect of a population.
Beta value
Type I errors & Type II errors
Conditional probability
Parameter
40. 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
Credence
quantitative variables
Residuals
Ratio measurements
41. Occurs when a subject receives no treatment - but (incorrectly) believes he or she is in fact receiving treatment and responds favorably.
A Distribution function
Qualitative variable
That value is the median value
Placebo effect
42. 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
inferential statistics
The sample space
variance of X
A random variable
43. 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
Correlation
hypotheses
Law of Large Numbers
Step 1 of a statistical experiment
44. Are usually written in upper case roman letters: X - Y - etc.
Sampling frame
Random variables
An experimental study
Inferential statistics
45. Used to reduce bias - this measure weights the more relevant information higher than less relevant info.
Pairwise independence
Statistical adjustment
That is the median value
Null hypothesis
46. 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.
That value is the median value
Descriptive statistics
Law of Parsimony
categorical variables
47. Is that part of a population which is actually observed.
Correlation coefficient
hypotheses
A sample
Conditional probability
48. To find the average - or arithmetic mean - of a set of numbers:
Step 2 of a statistical experiment
A data point
Divide the sum by the number of values.
Binomial experiment
49. 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
Divide the sum by the number of values.
Probability and statistics
A Distribution function
50. A scale that represents an ordinal scale such as looks on a scale from 1 to 10.
Alpha value (Level of Significance)
Parameter
the population cumulants
Likert scale