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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.
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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 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 experimental study
An event
Parameter
inferential statistics
2. E[X] :
expected value of X
The median value
The variance of a random variable
Conditional probability
3. Long-term upward or downward movement over time.
That value is the median value
Trend
An event
A population or statistical population
4. 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
the population cumulants
Conditional probability
Step 3 of a statistical experiment
observational study
5. Is the length of the smallest interval which contains all the data.
Alpha value (Level of Significance)
Law of Large Numbers
The Range
Placebo effect
6. Data are gathered and correlations between predictors and response are investigated.
Experimental and observational studies
Variable
A probability density function
observational study
7. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
Sampling frame
Probability density
Sampling Distribution
Residuals
8. Have no meaningful rank order among values.
Marginal probability
Nominal measurements
A probability space
Type II errors
9. 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.
The Expected value
Sampling
Observational study
Qualitative variable
10. 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.
Dependent Selection
An experimental study
An estimate of a parameter
A Distribution function
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.
Seasonal effect
Marginal probability
Inferential
Conditional probability
12. 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
The standard deviation
covariance of X and Y
Type 2 Error
13. (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.
Type 2 Error
Simulation
Cumulative distribution functions
An Elementary event
14. 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.
A likelihood function
Probability
Sampling frame
Independent Selection
15. 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
Valid measure
Statistical adjustment
hypotheses
An Elementary event
16. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
Power of a test
A probability distribution
Pairwise independence
Average and arithmetic mean
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'
The Expected value
Conditional probability
Marginal distribution
Valid measure
18. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
Likert scale
Law of Large Numbers
Descriptive
the sample or population mean
19. The probability of correctly detecting a false null hypothesis.
Power of a test
nominal - ordinal - interval - and ratio
Beta value
An event
20. Some commonly used symbols for sample statistics
Alpha value (Level of Significance)
Greek letters
Simpson's Paradox
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
21. Is defined as the expected value of random variable (X -
The Covariance between two random variables X and Y - with expected values E(X) =
hypotheses
Count data
Inferential statistics
22. (or multivariate random variable) is a vector whose components are random variables on the same probability space.
Observational study
hypotheses
Credence
A Random vector
23. 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
expected value of X
Conditional distribution
Conditional probability
24. Ratio and interval measurements which can be either discrete or continuous - due to their numerical nature are grouped together as
Valid measure
quantitative variables
A probability density function
Greek letters
25. ?
the population mean
A random variable
the population correlation
Simpson's Paradox
26. The proportion of the explained variation by a linear regression model in the total variation.
Residuals
Coefficient of determination
Treatment
Individual
27. 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}.
Nominal measurements
Type 1 Error
Credence
The sample space
28. 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.
Estimator
Inferential statistics
Sample space
Statistical dispersion
29. Var[X] :
The Mean of a random variable
The Covariance between two random variables X and Y - with expected values E(X) =
A population or statistical population
variance of X
30. (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
A likelihood function
Residuals
Standard error
Simple random sample
31. Statistics involve methods of using information from a sample to draw conclusions regarding the population.
observational study
Inferential
Binomial experiment
applied statistics
32. Also called correlation coefficient - is a numeric measure of the strength of linear relationship between two random variables (one can use it to quantify - for example - how shoe size and height are correlated in the population). An example is the P
An experimental study
Correlation
Bias
Marginal distribution
33. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.
Seasonal effect
s-algebras
Power of a test
Descriptive
34. 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.
Law of Parsimony
Simple random sample
A statistic
A random variable
35. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively
experimental studies and observational studies.
Residuals
A random variable
Standard error
36. 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.
Variability
Cumulative distribution functions
Particular realizations of a random variable
Dependent Selection
37. Describes the spread in the values of the sample statistic when many samples are taken.
the population variance
Type 1 Error
Variability
Nominal measurements
38. (also called statistical variability) is a measure of how diverse some data is. It can be expressed by the variance or the standard deviation.
Statistical dispersion
Variability
Power of a test
Marginal distribution
39. 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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40. Have imprecise differences between consecutive values - but have a meaningful order to those values
A data point
Law of Parsimony
Ordinal measurements
Average and arithmetic mean
41. Probability of accepting a false null hypothesis.
Lurking variable
The Mean of a random variable
Beta value
Law of Parsimony
42. A numerical measure that describes an aspect of a sample.
Statistic
Experimental and observational studies
Independence or Statistical independence
the population mean
43. A variable describes an individual by placing the individual into a category or a group.
A Statistical parameter
Simulation
Inferential
Qualitative variable
44. Occurs when a subject receives no treatment - but (incorrectly) believes he or she is in fact receiving treatment and responds favorably.
Bias
The standard deviation
Placebo effect
Observational study
45. 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
Block
Observational study
A Probability measure
Standard error
46. Many statistical methods seek to minimize the mean-squared error - and these are called
Divide the sum by the number of values.
Cumulative distribution functions
methods of least squares
Credence
47. A measurement such that the random error is small
Reliable measure
Correlation coefficient
Trend
Quantitative variable
48. Is a sample space over which a probability measure has been defined.
A probability space
A Distribution function
The Covariance between two random variables X and Y - with expected values E(X) =
the population variance
49. A data value that falls outside the overall pattern of the graph.
Outlier
experimental studies and observational studies.
Descriptive statistics
Ordinal measurements
50. Statistical methods can be used for summarizing or describing a collection of data; this is called
descriptive statistics
Probability density
s-algebras
Simulation
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