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Test your basic knowledge |
CLEP General Mathematics: Probability And Statistics
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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 written in corresponding lower case letters. For example x1 - x2 - ... - xn could be a sample corresponding to the random variable X.
Trend
Atomic event
A Distribution function
Particular realizations of a random variable
2. Are simply two different terms for the same thing. Add the given values
Average and arithmetic mean
observational study
A sampling distribution
covariance of X and Y
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
Skewness
Descriptive statistics
Sample space
hypothesis
4. Statistical methods can be used for summarizing or describing a collection of data; this is called
Credence
A probability density function
descriptive statistics
Statistics
5. Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically - sometimes they are grouped together as
categorical variables
Divide the sum by the number of values.
Descriptive statistics
the sample or population mean
6. The proportion of the explained variation by a linear regression model in the total variation.
Law of Large Numbers
Coefficient of determination
Atomic event
Dependent Selection
7. Is a function that gives the probability of all elements in a given space: see List of probability distributions
Conditional distribution
Statistical adjustment
A probability distribution
Binomial experiment
8. Some commonly used symbols for sample statistics
That value is the median value
Cumulative distribution functions
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Outlier
9. 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.
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10. 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 2 of a statistical experiment
An experimental study
Marginal distribution
The sample space
11. Descriptive statistics and inferential statistics (a.k.a. - predictive statistics) together comprise
A Distribution function
Joint distribution
applied statistics
categorical variables
12. (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.
Marginal distribution
Treatment
An Elementary event
Estimator
13. Gives the probability distribution for a continuous random variable.
A probability density function
Statistics
Descriptive
Step 3 of a statistical experiment
14. Consists of a number of independent trials repeated under identical conditions. On each trial - there are two possible outcomes.
A Statistical parameter
Binomial experiment
methods of least squares
An experimental study
15. Probability of rejecting a true null hypothesis.
Ratio measurements
Alpha value (Level of Significance)
Simulation
Independent Selection
16. Error also refers to the extent to which individual observations in a sample differ from a central value - such as
Variability
the sample or population mean
A Random vector
Random variables
17. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively
Posterior probability
Residuals
the population mean
Ratio measurements
18. Are usually written with upper case calligraphic (e.g. F for the set of sets on which we define the probability P)
Parameter
Sampling
s-algebras
methods of least squares
19. A data value that falls outside the overall pattern of the graph.
categorical variables
Probability density functions
Outlier
the population cumulants
20. A numerical measure that describes an aspect of a population.
The sample space
A probability density function
Parameter
Statistics
21. 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
Outlier
covariance of X and Y
hypotheses
the population cumulants
22. Is one that explores the correlation between smoking and lung cancer. This type of study typically uses a survey to collect observations about the area of interest and then performs statistical analysis. In this case - the researchers would collect o
descriptive statistics
Statistic
Observational study
Type 2 Error
23. 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
Step 1 of a statistical experiment
Count data
Lurking variable
A statistic
24. 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
covariance of X and Y
Conditional distribution
Step 3 of a statistical experiment
nominal - ordinal - interval - and ratio
25. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
Random variables
Likert scale
Step 3 of a statistical experiment
Prior probability
26. Probability of accepting a false null hypothesis.
Beta value
Estimator
observational study
Kurtosis
27. Long-term upward or downward movement over time.
Sampling
Trend
Simple random sample
Experimental and observational studies
28. (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
A statistic
Random variables
The Expected value
Interval measurements
29. Is data that can take only two values - usually represented by 0 and 1.
Binary data
Estimator
Binomial experiment
Mutual independence
30. 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.
Ratio measurements
Kurtosis
covariance of X and Y
Alpha value (Level of Significance)
31. (or multivariate random variable) is a vector whose components are random variables on the same probability space.
hypothesis
The median value
A Random vector
Skewness
32. 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
Posterior probability
Sampling frame
Skewness
A population or statistical population
33. Changes over time that show a regular periodicity in the data where regular means over a fixed interval; the time between repetitions is called the period.
Null hypothesis
Statistical adjustment
Type I errors
Seasonal effect
34. Used to reduce bias - this measure weights the more relevant information higher than less relevant info.
An experimental study
Independent Selection
Law of Parsimony
Statistical adjustment
35. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
A Random vector
nominal - ordinal - interval - and ratio
inferential statistics
Ratio measurements
36. 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)
Type I errors & Type II errors
The Range
Interval measurements
Observational study
37. When info. in a contingency table is re-organized into more or less categories - relationships seen can change or reverse.
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38. Cov[X - Y] :
nominal - ordinal - interval - and ratio
Ordinal measurements
covariance of X and Y
observational study
39. A group of individuals sharing some common features that might affect the treatment.
Pairwise independence
Block
nominal - ordinal - interval - and ratio
Independent Selection
40. Is a subset of the sample space - to which a probability can be assigned. For example - on rolling a die - 'getting a five or a six' is an event (with a probability of one third if the die is fair).
An event
The variance of a random variable
Step 1 of a statistical experiment
Skewness
41. 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
Independent Selection
A Random vector
Inferential
Mutual independence
42. Is data arising from counting that can take only non-negative integer values.
Binomial experiment
Count data
Nominal measurements
That is the median value
43. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
Law of Large Numbers
The average - or arithmetic mean
Ordinal measurements
Binary data
44. Is that part of a population which is actually observed.
Simpson's Paradox
A sample
Statistic
Statistical dispersion
45. The result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data
Posterior probability
A data set
Sampling frame
Type 2 Error
46. Ratio and interval measurements which can be either discrete or continuous - due to their numerical nature are grouped together as
An experimental study
quantitative variables
Statistical adjustment
Law of Parsimony
47. Have no meaningful rank order among values.
Type I errors
A Random vector
A data set
Nominal measurements
48. Is its expected value. The mean (or sample mean of a data set is just the average value.
Bias
The Mean of a random variable
Probability
Treatment
49. (e.g. ? - b) are commonly used to denote unknown parameters (population parameters).
Treatment
Greek letters
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Experimental and observational studies
50. When you have two or more competing models - choose the simpler of the two models.
Statistical adjustment
Law of Parsimony
Ratio measurements
experimental studies and observational studies.