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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. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
Sampling Distribution
Placebo effect
An experimental study
Prior probability
2. Cov[X - Y] :
Placebo effect
The average - or arithmetic mean
covariance of X and Y
Greek letters
3. Is the result of applying a statistical algorithm to a data set. It can also be described as an observable random variable.
A statistic
Type 1 Error
the population mean
Beta value
4. A data value that falls outside the overall pattern of the graph.
Outlier
Ratio measurements
Joint probability
Simpson's Paradox
5. Is the most commonly used measure of statistical dispersion. It is the square root of the variance - and is generally written s (sigma).
Variability
The standard deviation
The Range
A probability space
6. A measure that is relevant or appropriate as a representation of that property.
A population or statistical population
A probability density function
Valid measure
Joint probability
7. The standard deviation of a sampling distribution.
Statistical inference
Beta value
Random variables
Standard error
8. The collection of all possible outcomes in an experiment.
Sample space
The Expected value
Step 2 of a statistical experiment
Posterior probability
9. A sample selected in such a way that each individual is equally likely to be selected as well as any group of size n is equally likely to be selected.
Simple random sample
Parameter - or 'statistical parameter'
An event
the population cumulants
10. 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
observational study
Probability density
Simple random sample
The median value
11. 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
Atomic event
Statistical adjustment
the sample or population mean
Step 2 of a statistical experiment
12. Are simply two different terms for the same thing. Add the given values
Atomic event
Simple random sample
Conditional probability
Average and arithmetic mean
13. To find the average - or arithmetic mean - of a set of numbers:
Type II errors
Credence
Quantitative variable
Divide the sum by the number of values.
14. Of a group of numbers is the center point of all those number values.
expected value of X
Interval measurements
The average - or arithmetic mean
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
15. 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.
quantitative variables
A population or statistical population
The sample space
Type 2 Error
16. 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.
Type 2 Error
Trend
Statistics
variance of X
17. 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
Step 3 of a statistical experiment
Simpson's Paradox
Statistical inference
18. 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
Ratio measurements
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
An estimate of a parameter
Marginal distribution
19. 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.
Sampling
Outlier
A Probability measure
Binomial experiment
20. 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
Atomic event
Step 1 of a statistical experiment
Null hypothesis
Descriptive statistics
21. (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
nominal - ordinal - interval - and ratio
A probability density function
A probability distribution
The Expected value
22. Var[X] :
A random variable
observational study
variance of X
Simple random sample
23. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.
Inferential
An estimate of a parameter
Type 2 Error
Variable
24. Long-term upward or downward movement over time.
Experimental and observational studies
Marginal distribution
Null hypothesis
Trend
25. 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
Probability density
An experimental study
Null hypothesis
Independent Selection
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
Trend
A likelihood function
Observational study
Skewness
27. A numerical facsimilie or representation of a real-world phenomenon.
The Mean of a random variable
Simulation
Independence or Statistical independence
The Covariance between two random variables X and Y - with expected values E(X) =
28. (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.
An Elementary event
Skewness
Experimental and observational studies
Statistical adjustment
29. A variable has a value or numerical measurement for which operations such as addition or averaging make sense.
Quantitative variable
Type 2 Error
Statistic
Confounded variables
30. Failing to reject a false null hypothesis.
Step 1 of a statistical experiment
Sampling frame
A sample
Type 2 Error
31. Data are gathered and correlations between predictors and response are investigated.
the population mean
observational study
Coefficient of determination
A Random vector
32. 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.
Type II errors
Sample space
Marginal distribution
The median value
33. 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
Law of Parsimony
inferential statistics
Probability and statistics
A Probability measure
34. Used to reduce bias - this measure weights the more relevant information higher than less relevant info.
Type II errors
hypotheses
Statistical adjustment
Probability density
35. Given two random variables X and Y - the joint distribution of X and Y is the probability distribution of X and Y together.
A Distribution function
Inferential statistics
Alpha value (Level of Significance)
Joint distribution
36. Is a sample space over which a probability measure has been defined.
The median value
Statistical adjustment
Credence
A probability space
37. 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
Skewness
A Probability measure
Probability density
hypothesis
38. Is a function that gives the probability of all elements in a given space: see List of probability distributions
Sampling
The Expected value
A probability distribution
The Covariance between two random variables X and Y - with expected values E(X) =
39. Where the null hypothesis is falsely rejected giving a 'false positive'.
Type I errors
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Marginal distribution
Bias
40. 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.
A Statistical parameter
Experimental and observational studies
Kurtosis
experimental studies and observational studies.
41. Probability of rejecting a true null hypothesis.
Alpha value (Level of Significance)
applied statistics
inferential statistics
Correlation coefficient
42. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
Independent Selection
Block
hypothesis
Sampling Distribution
43. Consists of a number of independent trials repeated under identical conditions. On each trial - there are two possible outcomes.
Observational study
Individual
Binomial experiment
An event
44. Where the null hypothesis fails to be rejected and an actual difference between populations is missed giving a 'false negative'.
The median value
Variable
The Expected value
Type II errors
45. Statistics involve methods of using information from a sample to draw conclusions regarding the population.
Inferential
Probability density
An estimate of a parameter
An event
46. When there is an even number of values...
the population correlation
Cumulative distribution functions
That is the median value
A data set
47. 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.
Joint distribution
Simulation
Seasonal effect
Particular realizations of a random variable
48. 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.
Sampling frame
Independent Selection
Estimator
Power of a test
49. 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.
Descriptive statistics
Estimator
Random variables
A likelihood function
50. (pdfs) and probability mass functions are denoted by lower case letters - e.g. f(x).
Seasonal effect
Experimental and observational studies
P-value
Probability density functions