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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. Another name for elementary event.
Interval measurements
Outlier
observational study
Atomic event
2. A numerical measure that assesses the strength of a linear relationship between two variables.
Joint distribution
Lurking variable
Correlation coefficient
The Expected value
3. A consistent - repeated deviation of the sample statistic from the population parameter in the same direction when many samples are taken.
The average - or arithmetic mean
Bias
experimental studies and observational studies.
Outlier
4. To find the average - or arithmetic mean - of a set of numbers:
An Elementary event
Divide the sum by the number of values.
The Range
the population cumulants
5. 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'
Coefficient of determination
A Distribution function
Law of Parsimony
Conditional probability
6. The collection of all possible outcomes in an experiment.
Sample space
Step 2 of a statistical experiment
Divide the sum by the number of values.
An experimental study
7. 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.
Simple random sample
nominal - ordinal - interval - and ratio
A random variable
Statistical dispersion
8. Error also refers to the extent to which individual observations in a sample differ from a central value - such as
Correlation
the sample or population mean
An event
the population correlation
9. Failing to reject a false null hypothesis.
Observational study
An event
Type 2 Error
Simpson's Paradox
10. Is denoted by - pronounced 'x bar'.
A Probability measure
the population mean
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Inferential statistics
11. S^2
Sampling Distribution
Residuals
A probability distribution
the population variance
12. 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.
Power of a test
Pairwise independence
Descriptive
Statistical inference
13. 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.
Type II errors
A Distribution function
Type I errors & Type II errors
Random variables
14. Are usually written with upper case calligraphic (e.g. F for the set of sets on which we define the probability P)
applied statistics
the population variance
Simulation
s-algebras
15. Are simply two different terms for the same thing. Add the given values
Average and arithmetic mean
experimental studies and observational studies.
Estimator
Step 2 of a statistical experiment
16. A variable describes an individual by placing the individual into a category or a group.
Qualitative variable
Simulation
Bias
Estimator
17. Is a sample space over which a probability measure has been defined.
A probability space
Average and arithmetic mean
Greek letters
Statistical adjustment
18. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
Step 3 of a statistical experiment
Descriptive
Credence
P-value
19. 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.
nominal - ordinal - interval - and ratio
Independent Selection
Quantitative variable
The median value
20. Have imprecise differences between consecutive values - but have a meaningful order to those values
Ordinal measurements
Pairwise independence
Probability density functions
Sample space
21. Where the null hypothesis fails to be rejected and an actual difference between populations is missed giving a 'false negative'.
observational study
Statistical inference
Type II errors
Individual
22. (cdfs) are denoted by upper case letters - e.g. F(x).
nominal - ordinal - interval - and ratio
Cumulative distribution functions
Qualitative variable
Outlier
23. 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 Mean of a random variable
inferential statistics
Cumulative distribution functions
A probability distribution
24. A data value that falls outside the overall pattern of the graph.
The Mean of a random variable
Outlier
A Random vector
Probability density
25. A collection of events is mutually independent if for any subset of the collection - the joint probability of all events occurring is equal to the product of the joint probabilities of the individual events. Think of the result of a series of coin-fl
That is the median value
s-algebras
Mutual independence
variance of X
26. 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
Skewness
Statistics
Reliable measure
Correlation
27. 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
Step 2 of a statistical experiment
P-value
experimental studies and observational studies.
28. Gives the probability of events in a probability space.
A Probability measure
An experimental study
Ordinal measurements
the population correlation
29. (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
Statistic
A Random vector
A likelihood function
The Range
30. (e.g. ? - b) are commonly used to denote unknown parameters (population parameters).
Bias
Greek letters
Skewness
the population cumulants
31. 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
Probability density
Kurtosis
Type 2 Error
Average and arithmetic mean
32. The proportion of the explained variation by a linear regression model in the total variation.
Coefficient of determination
Estimator
the population correlation
variance of X
33. A numerical facsimilie or representation of a real-world phenomenon.
the population mean
A Probability measure
covariance of X and Y
Simulation
34. (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.
A probability space
Statistic
Standard error
An Elementary event
35. Are usually written in upper case roman letters: X - Y - etc.
Sampling frame
Random variables
An event
Joint distribution
36. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.
Type I errors & Type II errors
An estimate of a parameter
Ordinal measurements
Descriptive
37. In particular - the pdf of the standard normal distribution is denoted by
the population variance
Correlation coefficient
descriptive statistics
f(z) - and its cdf by F(z).
38. Cov[X - Y] :
covariance of X and Y
An estimate of a parameter
Probability and statistics
A population or statistical population
39. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
inferential statistics
Conditional probability
Sampling Distribution
A random variable
40. Is a sample and the associated data points.
Type I errors
Correlation
A data set
That value is the median value
41. (also called statistical variability) is a measure of how diverse some data is. It can be expressed by the variance or the standard deviation.
f(z) - and its cdf by F(z).
Statistical dispersion
A random variable
the population mean
42. Gives the probability distribution for a continuous random variable.
A probability density function
Sample space
Binary data
Statistical inference
43. A measurement such that the random error is small
The median value
The Mean of a random variable
Divide the sum by the number of values.
Reliable measure
44. The result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data
Residuals
Posterior probability
Treatment
That is the median value
45. Is the probability of an event - ignoring any information about other events. The marginal probability of A is written P(A). Contrast with conditional probability.
Marginal probability
Individual
Parameter - or 'statistical parameter'
variance of X
46. A common goal for a statistical research project is to investigate causality - and in particular to draw a conclusion on the effect of changes in the values of predictors or independent variables on dependent variables or response.
A sampling distribution
Treatment
Atomic event
Experimental and observational studies
47. 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).
Dependent Selection
Sampling frame
Mutual independence
An event
48. Is that part of a population which is actually observed.
Conditional probability
Step 2 of a statistical experiment
A sample
expected value of X
49. Long-term upward or downward movement over time.
Correlation coefficient
A probability density function
Trend
Seasonal effect
50. Statistics involve methods of using information from a sample to draw conclusions regarding the population.
covariance of X and Y
Count data
Inferential
Ordinal measurements