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Test your basic knowledge |
CLEP General Mathematics: Probability And Statistics
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Subjects
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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
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. Error also refers to the extent to which individual observations in a sample differ from a central value - such as
the sample or population mean
A statistic
Random variables
Sampling frame
2. (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.
Observational study
experimental studies and observational studies.
f(z) - and its cdf by F(z).
An Elementary event
3. Some commonly used symbols for population parameters
A sampling distribution
A Random vector
A Distribution function
the population mean
4. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
Interval measurements
Statistical inference
Type I errors
Pairwise independence
5. 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).
A Statistical parameter
Cumulative distribution functions
Variability
Joint probability
6. The collection of all possible outcomes in an experiment.
Sample space
categorical variables
Step 3 of a statistical experiment
Statistical inference
7. 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
Sampling frame
covariance of X and Y
A random variable
Mutual independence
8. S^2
Standard error
the population variance
Variability
Seasonal effect
9. Statistics involve methods of using information from a sample to draw conclusions regarding the population.
Simpson's Paradox
Inferential
Variable
f(z) - and its cdf by F(z).
10. 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
Sampling frame
Descriptive
Step 3 of a statistical experiment
Simple random sample
11. 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.
Independent Selection
A Distribution function
Atomic event
Binomial experiment
12. Ratio and interval measurements which can be either discrete or continuous - due to their numerical nature are grouped together as
Inferential statistics
A Probability measure
A data point
quantitative variables
13. 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
Correlation coefficient
A random variable
Ratio measurements
observational study
14. The probability of correctly detecting a false null hypothesis.
the population cumulants
Power of a test
The standard deviation
Step 1 of a statistical experiment
15. Are usually written in upper case roman letters: X - Y - etc.
Random variables
Interval measurements
Binomial experiment
Sampling
16. Failing to reject a false null hypothesis.
Type 2 Error
variance of X
expected value of X
Coefficient of determination
17. Given two random variables X and Y - the joint distribution of X and Y is the probability distribution of X and Y together.
An Elementary event
expected value of X
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Joint distribution
18. Gives the probability of events in a probability space.
A Probability measure
Average and arithmetic mean
Step 1 of a statistical experiment
The Range
19. Used to reduce bias - this measure weights the more relevant information higher than less relevant info.
Experimental and observational studies
Statistical adjustment
Valid measure
Placebo effect
20. Involves taking measurements of the system under study - manipulating the system - and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements.
A Random vector
Qualitative variable
observational study
An experimental study
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.
Trend
Marginal distribution
Outlier
Pairwise independence
22. Is data arising from counting that can take only non-negative integer values.
Count data
The Covariance between two random variables X and Y - with expected values E(X) =
expected value of X
That is the median value
23. (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
Variable
A likelihood function
Step 2 of a statistical experiment
Statistic
24. The proportion of the explained variation by a linear regression model in the total variation.
Cumulative distribution functions
An experimental study
A Random vector
Coefficient of determination
25. Two events are independent if the outcome of one does not affect that of the other (for example - getting a 1 on one die roll does not affect the probability of getting a 1 on a second roll). Similarly - when we assert that two random variables are i
Joint probability
Observational study
A probability space
Independence or Statistical independence
26. Summarize the population data by describing what was observed in the sample numerically or graphically. Numerical descriptors include mean and standard deviation for continuous data types (like heights or weights) - while frequency and percentage are
Pairwise independence
Statistics
Descriptive statistics
Prior probability
27. 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
Probability and statistics
Skewness
Step 2 of a statistical experiment
A Probability measure
28. 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
Bias
A probability space
Statistic
Inferential statistics
29. 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)
A Distribution function
Nominal measurements
Interval measurements
categorical variables
30. A numerical measure that describes an aspect of a sample.
Reliable measure
the sample or population mean
Statistic
Descriptive statistics
31. A measure that is relevant or appropriate as a representation of that property.
Valid measure
Nominal measurements
Descriptive
Skewness
32. Long-term upward or downward movement over time.
descriptive statistics
Block
Trend
Correlation
33. Descriptive statistics and inferential statistics (a.k.a. - predictive statistics) together comprise
Seasonal effect
Skewness
applied statistics
Ratio measurements
34. 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.
Probability and statistics
A Statistical parameter
Marginal probability
inferential statistics
35. (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
Treatment
The Expected value
A data point
Observational study
36. Is defined as the expected value of random variable (X -
A sample
Kurtosis
The Covariance between two random variables X and Y - with expected values E(X) =
Coefficient of determination
37. Is denoted by - pronounced 'x bar'.
hypothesis
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Individual
the population cumulants
38. Is data that can take only two values - usually represented by 0 and 1.
categorical variables
Type 1 Error
Experimental and observational studies
Binary data
39. 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.
Type I errors & Type II errors
P-value
experimental studies and observational studies.
The median value
40. 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
Credence
Count data
An experimental study
41. 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.
Correlation coefficient
Experimental and observational studies
An event
Marginal probability
42. 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}.
Valid measure
Step 3 of a statistical experiment
The sample space
Placebo effect
43. 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.
Step 2 of a statistical experiment
Marginal probability
covariance of X and Y
Independent Selection
44. To prove the guiding theory further - these predictions are tested as well - as part of the scientific method. If the inference holds true - then the descriptive statistics of the new data increase the soundness of that
An estimate of a parameter
Joint probability
The average - or arithmetic mean
hypothesis
45. 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
Kurtosis
Posterior probability
Quantitative variable
hypotheses
46. Are usually written with upper case calligraphic (e.g. F for the set of sets on which we define the probability P)
A Distribution function
Law of Large Numbers
s-algebras
Interval measurements
47. A data value that falls outside the overall pattern of the graph.
Estimator
Outlier
Conditional probability
the population variance
48. 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
Conditional distribution
applied statistics
An Elementary event
Observational study
49. Occurs when a subject receives no treatment - but (incorrectly) believes he or she is in fact receiving treatment and responds favorably.
Descriptive
The Mean of a random variable
Pairwise independence
Placebo effect
50. Is the probability distribution - under repeated sampling of the population - of a given statistic.
s-algebras
Outlier
A sampling distribution
Alpha value (Level of Significance)