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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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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. 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
Probability
The median value
A Random vector
Bias
2. 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.
Bias
Individual
Joint probability
Law of Large Numbers
3. Is the probability distribution - under repeated sampling of the population - of a given statistic.
Independent Selection
A sampling distribution
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Descriptive
4. 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.
A random variable
Parameter
Treatment
Valid measure
5. (pdfs) and probability mass functions are denoted by lower case letters - e.g. f(x).
Quantitative variable
Probability
Probability density functions
Skewness
6. When there is an even number of values...
Credence
Independence or Statistical independence
That is the median value
Statistical dispersion
7. Is its expected value. The mean (or sample mean of a data set is just the average value.
Probability and statistics
expected value of X
A likelihood function
The Mean of a random variable
8. Working from a null hypothesis two basic forms of error are recognized:
Type I errors & Type II errors
That value is the median value
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
observational study
9. A variable has a value or numerical measurement for which operations such as addition or averaging make sense.
Standard error
Quantitative variable
A data point
Dependent Selection
10. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
A sampling distribution
Kurtosis
Prior probability
Conditional probability
11. Another name for elementary event.
variance of X
Atomic event
Interval measurements
the population cumulants
12. 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 population or statistical population
The Expected value
Estimator
hypothesis
13. Descriptive statistics and inferential statistics (a.k.a. - predictive statistics) together comprise
A Probability measure
Greek letters
An event
applied statistics
14. A measurement such that the random error is small
Residuals
Sample space
Reliable measure
Inferential
15. Is a sample space over which a probability measure has been defined.
A probability space
the population variance
A Distribution function
Statistic
16. 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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17. Of a group of numbers is the center point of all those number values.
s-algebras
Outlier
The average - or arithmetic mean
Variability
18. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
methods of least squares
Sampling Distribution
expected value of X
The median value
19. 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
f(z) - and its cdf by F(z).
hypotheses
applied statistics
Block
20. A numerical measure that describes an aspect of a sample.
Skewness
Statistic
Sampling frame
The sample space
21. 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.
Marginal distribution
Inferential statistics
Count data
the population mean
22. 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
the population cumulants
Sample space
inferential statistics
s-algebras
23. 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.
Step 1 of a statistical experiment
The median value
Ordinal measurements
Valid measure
24. The objects described by a set of data: person (animal) - place - and - thing. (SUBJECTS)
Individual
s-algebras
An experimental study
Standard error
25. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
Observational study
An event
Pairwise independence
Outlier
26. 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.
Step 2 of a statistical experiment
Parameter
Inferential statistics
Kurtosis
27. The probability of correctly detecting a false null hypothesis.
Power of a test
the population mean
Probability density functions
A sampling distribution
28. The result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data
Probability density
Quantitative variable
Statistical inference
Posterior probability
29. Some commonly used symbols for population parameters
A Statistical parameter
the population mean
Dependent Selection
Posterior probability
30. Any specific experimental condition applied to the subjects
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Treatment
Type 1 Error
The Covariance between two random variables X and Y - with expected values E(X) =
31. Two variables such that their effects on the response variable cannot be distinguished from each other.
P-value
Cumulative distribution functions
Simple random sample
Confounded variables
32. S^2
Credence
The Mean of a random variable
the population variance
categorical variables
33. 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)
P-value
Inferential statistics
Probability and statistics
Interval measurements
34. Is data arising from counting that can take only non-negative integer values.
Type I errors
Estimator
Count data
the population variance
35. 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.
Posterior probability
Simple random sample
Conditional distribution
Sampling Distribution
36. Probability of accepting a false null hypothesis.
The Expected value
Joint probability
Beta value
applied statistics
37. Gives the probability distribution for a continuous random variable.
Descriptive
Quantitative variable
A probability density function
Valid measure
38. A measure that is relevant or appropriate as a representation of that property.
Valid measure
A probability density function
Binary data
Seasonal effect
39. (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
Valid measure
The Expected value
Descriptive statistics
Kurtosis
40. E[X] :
Simpson's Paradox
Coefficient of determination
expected value of X
Law of Large Numbers
41. Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically - sometimes they are grouped together as
Null hypothesis
hypothesis
Standard error
categorical variables
42. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively
An experimental study
Probability density
Residuals
Coefficient of determination
43. A numerical measure that assesses the strength of a linear relationship between two variables.
nominal - ordinal - interval - and ratio
Correlation coefficient
Independence or Statistical independence
Type II errors
44. A group of individuals sharing some common features that might affect the treatment.
Reliable measure
Statistical adjustment
Block
the population mean
45. Is that part of a population which is actually observed.
Nominal measurements
f(z) - and its cdf by F(z).
A sample
A data set
46. Ratio and interval measurements which can be either discrete or continuous - due to their numerical nature are grouped together as
s-algebras
Simpson's Paradox
quantitative variables
The Expected value
47. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.
Count data
An estimate of a parameter
Mutual independence
A Random vector
48.
Pairwise independence
Treatment
the population mean
Probability and statistics
49. Failing to reject a false null hypothesis.
Individual
Inferential
A probability density function
Type 2 Error
50. Samples are drawn from two different populations such that there is a matching of the first sample data drawn and a corresponding data value in the second sample data.
Dependent Selection
Variability
Prior probability
Step 1 of a statistical experiment