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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. 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
Joint probability
Likert scale
Descriptive
Probability and statistics
2. 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
Average and arithmetic mean
Step 2 of a statistical experiment
Null hypothesis
Type I errors & Type II errors
3. 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.
Null hypothesis
Marginal distribution
Ordinal measurements
descriptive statistics
4. Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically - sometimes they are grouped together as
A probability distribution
Independent Selection
P-value
categorical variables
5. A numerical measure that describes an aspect of a sample.
Statistic
Beta value
Greek letters
Step 1 of a statistical experiment
6. Consists of a number of independent trials repeated under identical conditions. On each trial - there are two possible outcomes.
Type I errors & Type II errors
descriptive statistics
Seasonal effect
Binomial experiment
7. Error also refers to the extent to which individual observations in a sample differ from a central value - such as
Marginal probability
Bias
the sample or population mean
Alpha value (Level of Significance)
8. Is a parameter that indexes a family of probability distributions.
A Statistical parameter
Statistics
Law of Large Numbers
applied statistics
9. Probability of accepting a false null hypothesis.
Beta value
Law of Parsimony
Marginal distribution
Parameter - or 'statistical parameter'
10. Is the probability distribution - under repeated sampling of the population - of a given statistic.
the population mean
A sampling distribution
Simpson's Paradox
Quantitative variable
11. 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.
The median value
the population mean
Seasonal effect
Power of a test
12. Where the null hypothesis is falsely rejected giving a 'false positive'.
Type I errors
Treatment
Binomial experiment
The variance of a random variable
13. When you have two or more competing models - choose the simpler of the two models.
Law of Parsimony
Type I errors
A probability space
methods of least squares
14. S^2
The average - or arithmetic mean
hypothesis
Coefficient of determination
the population variance
15. Some commonly used symbols for sample statistics
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Probability density functions
Step 3 of a statistical experiment
An experimental study
16. Of a group of numbers is the center point of all those number values.
The average - or arithmetic mean
Posterior probability
Variable
Parameter - or 'statistical parameter'
17. (also called statistical variability) is a measure of how diverse some data is. It can be expressed by the variance or the standard deviation.
Probability density functions
Nominal measurements
Statistical dispersion
Joint distribution
18. Many statistical methods seek to minimize the mean-squared error - and these are called
inferential statistics
methods of least squares
Simulation
the population mean
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.
Descriptive statistics
Outlier
Sampling
Estimator
20. 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.
Estimator
A population or statistical population
Cumulative distribution functions
A random variable
21. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
Sample space
Prior probability
An Elementary event
Null hypothesis
22. Cov[X - Y] :
covariance of X and Y
Power of a test
The variance of a random variable
Individual
23. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
Sampling Distribution
categorical variables
The median value
Statistical dispersion
24. Describes a characteristic of an individual to be measured or observed.
Variable
Observational study
Power of a test
A random variable
25. 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.
Skewness
categorical variables
inferential statistics
Statistical inference
26. Is the function that gives the probability distribution of a random variable. It cannot be negative - and its integral on the probability space is equal to 1.
the population cumulants
A Distribution function
A Probability measure
Particular realizations of a random variable
27. In particular - the pdf of the standard normal distribution is denoted by
Nominal measurements
Independence or Statistical independence
Conditional probability
f(z) - and its cdf by F(z).
28. A consistent - repeated deviation of the sample statistic from the population parameter in the same direction when many samples are taken.
Statistical inference
Confounded variables
Bias
Type I errors
29. Is defined as the expected value of random variable (X -
Independent Selection
Law of Large Numbers
The Covariance between two random variables X and Y - with expected values E(X) =
A Statistical parameter
30. 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.
The Expected value
Reliable measure
Statistics
Coefficient of determination
31. 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
Posterior probability
Beta value
The standard deviation
32. Is its expected value. The mean (or sample mean of a data set is just the average value.
The Mean of a random variable
Simple random sample
Quantitative variable
Lurking variable
33. Is data that can take only two values - usually represented by 0 and 1.
Binary data
Qualitative variable
Inferential
inferential statistics
34. A measurement such that the random error is small
The average - or arithmetic mean
Reliable measure
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
An estimate of a parameter
35. 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
Step 3 of a statistical experiment
Sampling
Estimator
Trend
36. (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
Step 2 of a statistical experiment
Ordinal measurements
The Expected value
The sample space
37. Statistical methods can be used for summarizing or describing a collection of data; this is called
Seasonal effect
descriptive statistics
Atomic event
Probability and statistics
38. (cdfs) are denoted by upper case letters - e.g. F(x).
Confounded variables
Simulation
Reliable measure
Cumulative distribution functions
39. 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.
Lurking variable
Individual
Bias
The variance of a random variable
40. E[X] :
hypothesis
expected value of X
Joint distribution
Statistical dispersion
41. Failing to reject a false null hypothesis.
Type 2 Error
A data point
Random variables
quantitative variables
42. 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.
The Range
Estimator
Simpson's Paradox
Standard error
43. Is the most commonly used measure of statistical dispersion. It is the square root of the variance - and is generally written s (sigma).
expected value of X
Kurtosis
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
The standard deviation
44. 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.
A population or statistical population
Simple random sample
Simulation
Statistic
45. Is used in 'mathematical statistics' (alternatively - 'statistical theory') to study the sampling distributions of sample statistics and - more generally - the properties of statistical procedures. The use of any statistical method is valid when the
Qualitative variable
Statistical dispersion
An estimate of a parameter
Probability
46. Occurs when a subject receives no treatment - but (incorrectly) believes he or she is in fact receiving treatment and responds favorably.
the sample or population mean
Placebo effect
nominal - ordinal - interval - and ratio
Pairwise independence
47. The collection of all possible outcomes in an experiment.
A probability space
Sample space
A Probability measure
inferential statistics
48. The result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data
Bias
Simpson's Paradox
covariance of X and Y
Posterior probability
49. 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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50. The probability of correctly detecting a false null hypothesis.
Step 1 of a statistical experiment
Power of a test
Inferential
the population mean