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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.
If you are not ready to take this test, you can
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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 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
Individual
Statistical adjustment
2. 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.
Statistic
Atomic event
Marginal distribution
Inferential statistics
3. Are written in corresponding lower case letters. For example x1 - x2 - ... - xn could be a sample corresponding to the random variable X.
Estimator
applied statistics
Particular realizations of a random variable
A probability space
4. Is the probability of two events occurring together. The joint probability of A and B is written P(A and B) or P(A - B).
An experimental study
Block
Joint probability
quantitative variables
5. Is a parameter that indexes a family of probability distributions.
Simulation
Alpha value (Level of Significance)
A Statistical parameter
The standard deviation
6. The result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data
A probability space
methods of least squares
Posterior probability
Trend
7. (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
Qualitative variable
A probability distribution
A likelihood function
the population correlation
8. (pdfs) and probability mass functions are denoted by lower case letters - e.g. f(x).
Alpha value (Level of Significance)
applied statistics
Count data
Probability density functions
9. 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
Observational study
Type 2 Error
Average and arithmetic mean
Inferential statistics
10. Is the most commonly used measure of statistical dispersion. It is the square root of the variance - and is generally written s (sigma).
Standard error
quantitative variables
the population variance
The standard deviation
11. 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.
Kurtosis
Step 3 of a statistical experiment
Null hypothesis
Conditional distribution
12. (e.g. ? - b) are commonly used to denote unknown parameters (population parameters).
An experimental study
Average and arithmetic mean
Random variables
Greek letters
13. 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 Statistical parameter
A data set
Simple random sample
Residuals
14. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
A Statistical parameter
P-value
Random variables
f(z) - and its cdf by F(z).
15. 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
A probability space
An experimental study
applied statistics
Probability density
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.
Block
Statistical inference
Statistics
P-value
17. (cdfs) are denoted by upper case letters - e.g. F(x).
Pairwise independence
Type I errors & Type II errors
the population cumulants
Cumulative distribution functions
18. Describes the spread in the values of the sample statistic when many samples are taken.
Statistic
Type 2 Error
Variability
Nominal measurements
19. Another name for elementary event.
categorical variables
That is the median value
Atomic event
Statistical inference
20. (or multivariate random variable) is a vector whose components are random variables on the same probability space.
The Range
Correlation
A Random vector
The Covariance between two random variables X and Y - with expected values E(X) =
21. ?
The sample space
the population correlation
Individual
the population variance
22. Rejecting a true null hypothesis.
the population correlation
Null hypothesis
Type 1 Error
Skewness
23. Is data that can take only two values - usually represented by 0 and 1.
Lurking variable
Binary data
Posterior probability
Credence
24. Any specific experimental condition applied to the subjects
Treatment
An experimental study
A population or statistical population
covariance of X and Y
25. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.
the population mean
An estimate of a parameter
A data set
Correlation coefficient
26. 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
Descriptive statistics
Conditional probability
Count data
Inferential statistics
27. 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
The standard deviation
Posterior probability
Skewness
Joint probability
28. Probability of accepting a false null hypothesis.
A Random vector
Beta value
Cumulative distribution functions
Step 3 of a statistical experiment
29. Is the length of the smallest interval which contains all the data.
Average and arithmetic mean
The Range
Residuals
descriptive statistics
30. Two variables such that their effects on the response variable cannot be distinguished from each other.
Confounded variables
Reliable measure
Type 1 Error
A Probability measure
31. 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.
Skewness
the population cumulants
the sample or population mean
A data point
32. A data value that falls outside the overall pattern of the graph.
A data set
An event
Outlier
hypotheses
33. (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
Placebo effect
The Expected value
The variance of a random variable
The Range
34. Is defined as the expected value of random variable (X -
Cumulative distribution functions
the population mean
The Covariance between two random variables X and Y - with expected values E(X) =
Type II errors
35. A subjective estimate of probability.
categorical variables
Correlation
Credence
Individual
36. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
Pairwise independence
nominal - ordinal - interval - and ratio
Bias
The sample space
37. A numerical measure that describes an aspect of a sample.
Sample space
Statistic
Ordinal measurements
Type I errors & Type II errors
38. Failing to reject a false null hypothesis.
Independence or Statistical independence
Skewness
Block
Type 2 Error
39. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
Sampling Distribution
An Elementary event
Coefficient of determination
Statistical inference
40. Of a group of numbers is the center point of all those number values.
The average - or arithmetic mean
Binary data
Divide the sum by the number of values.
the sample or population mean
41. There are two major types of causal statistical studies: In both types of studies - the effect of differences of an independent variable (or variables) on the behavior of the dependent variable are observed. The difference between the two types lies
experimental studies and observational studies.
Marginal distribution
Type I errors & Type II errors
Individual
42. 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.
Parameter
A Distribution function
A sample
Particular realizations of a random variable
43. Is denoted by - pronounced 'x bar'.
Step 3 of a statistical experiment
Variable
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Interval measurements
44. Is the probability distribution - under repeated sampling of the population - of a given statistic.
The Mean of a random variable
A sampling distribution
hypotheses
Binomial experiment
45. 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
Standard error
A probability density function
Independent Selection
46. 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
inferential statistics
Prior probability
Power of a test
Bias
47. Used to reduce bias - this measure weights the more relevant information higher than less relevant info.
Marginal distribution
Statistical adjustment
Sample space
Credence
48. Is a sample space over which a probability measure has been defined.
Type II errors
A probability space
quantitative variables
That is the median value
49. 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
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
A data set
Null hypothesis
experimental studies and observational studies.
50. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively
Residuals
the population mean
The Expected value
An experimental study