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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. 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
An event
Estimator
A sample
Step 2 of a statistical experiment
2. 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
A data set
Statistical dispersion
Statistical adjustment
3.
Placebo effect
the population mean
Statistical adjustment
An estimate of a parameter
4. When there is an even number of values...
A Random vector
That is the median value
inferential statistics
The Expected value
5. Var[X] :
Type I errors & Type II errors
variance of X
covariance of X and Y
A likelihood function
6. 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
Quantitative variable
Mutual independence
A population or statistical population
Joint distribution
7. Have no meaningful rank order among values.
Nominal measurements
Parameter
observational study
Probability density functions
8. 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).
Conditional probability
Prior probability
An event
Statistical dispersion
9. 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.
Binary data
Variable
Lurking variable
That value is the median value
10. Are usually written in upper case roman letters: X - Y - etc.
Random variables
Interval measurements
Descriptive statistics
An Elementary event
11. (cdfs) are denoted by upper case letters - e.g. F(x).
A Statistical parameter
descriptive statistics
Quantitative variable
Cumulative distribution functions
12. Used to reduce bias - this measure weights the more relevant information higher than less relevant info.
Statistical adjustment
Greek letters
observational study
A sample
13. 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.
Pairwise independence
Greek letters
The Expected value
Kurtosis
14. 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.
Posterior probability
A data point
Nominal measurements
A population or statistical population
15. 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
Skewness
The median value
hypotheses
Simple random sample
16. Is that part of a population which is actually observed.
Statistical dispersion
A sampling distribution
A sample
Statistics
17. 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.
A probability distribution
Parameter
Correlation coefficient
A population or statistical population
18. A numerical measure that describes an aspect of a population.
Parameter
Independence or Statistical independence
Qualitative variable
Sampling Distribution
19. Describes a characteristic of an individual to be measured or observed.
Interval measurements
Statistical inference
Variable
Coefficient of determination
20. Given two random variables X and Y - the joint distribution of X and Y is the probability distribution of X and Y together.
Type I errors
Joint distribution
Lurking variable
A Distribution function
21. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
Inferential
nominal - ordinal - interval - and ratio
Trend
Step 1 of a statistical experiment
22. Ratio and interval measurements which can be either discrete or continuous - due to their numerical nature are grouped together as
The average - or arithmetic mean
quantitative variables
Inferential
Marginal distribution
23. Is a parameter that indexes a family of probability distributions.
Treatment
The median value
A Statistical parameter
Bias
24. 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
Observational study
A statistic
Step 3 of a statistical experiment
25. Gives the probability of events in a probability space.
A Probability measure
Dependent Selection
Sample space
Binomial experiment
26. 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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27. 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.
Observational study
An experimental study
Ratio measurements
Independent Selection
28. 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 variance of a random variable
Marginal distribution
The sample space
Joint probability
29. A group of individuals sharing some common features that might affect the treatment.
Block
Atomic event
Treatment
A population or statistical population
30. (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
covariance of X and Y
Standard error
the population variance
The Expected value
31. Is a sample space over which a probability measure has been defined.
Law of Parsimony
Estimator
A probability space
A statistic
32. A variable describes an individual by placing the individual into a category or a group.
An event
Qualitative variable
That is the median value
A Random vector
33. Where the null hypothesis is falsely rejected giving a 'false positive'.
Posterior probability
Type I errors
Ratio measurements
the population mean
34. A common goal for a statistical research project is to investigate causality - and in particular to draw a conclusion on the effect of changes in the values of predictors or independent variables on dependent variables or response.
Statistical adjustment
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
quantitative variables
Experimental and observational studies
35. To find the average - or arithmetic mean - of a set of numbers:
Probability and statistics
Ratio measurements
Divide the sum by the number of values.
Statistic
36. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively
Law of Large Numbers
Correlation
Residuals
That is the median value
37. Samples are drawn from two different populations such that the sample data drawn from one population is completely unrelated to the selection of sample data from the other population.
Random variables
An event
Independent Selection
Likert scale
38. Some commonly used symbols for population parameters
Simpson's Paradox
A probability density function
the population mean
observational study
39. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.
Greek letters
Step 2 of a statistical experiment
An estimate of a parameter
Conditional probability
40. When you have two or more competing models - choose the simpler of the two models.
Observational study
Correlation
Simple random sample
Law of Parsimony
41. A variable has a value or numerical measurement for which operations such as addition or averaging make sense.
Null hypothesis
Statistical dispersion
Quantitative variable
Probability density functions
42. A numerical measure that describes an aspect of a sample.
expected value of X
Statistical inference
Variability
Statistic
43. Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically - sometimes they are grouped together as
Independent Selection
Treatment
categorical variables
Parameter
44. A data value that falls outside the overall pattern of the graph.
Binomial experiment
Reliable measure
Count data
Outlier
45. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
Prior probability
Experimental and observational studies
Law of Large Numbers
nominal - ordinal - interval - and ratio
46. 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
Bias
Power of a test
applied statistics
Step 3 of a statistical experiment
47. (also called statistical variability) is a measure of how diverse some data is. It can be expressed by the variance or the standard deviation.
s-algebras
applied statistics
observational study
Statistical dispersion
48. Is used to describe probability in a continuous probability distribution. For example - you can't say that the probability of a man being six feet tall is 20% - but you can say he has 20% of chances of being between five and six feet tall. Probabilit
Treatment
s-algebras
hypothesis
Probability density
49. Have imprecise differences between consecutive values - but have a meaningful order to those values
Ordinal measurements
descriptive statistics
The median value
Confounded variables
50. A scale that represents an ordinal scale such as looks on a scale from 1 to 10.
Likert scale
An Elementary event
Inferential statistics
Correlation coefficient