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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. Some commonly used symbols for sample statistics
An event
categorical variables
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
The Mean of a random variable
2. 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
Alpha value (Level of Significance)
The standard deviation
Mutual independence
Skewness
3. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
Seasonal effect
Joint probability
Type I errors & Type II errors
Sampling Distribution
4. 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
Mutual independence
Descriptive
Residuals
Statistics
5. Statistics involve methods of using information from a sample to draw conclusions regarding the population.
Inferential
The Range
Statistical dispersion
the population mean
6. The proportion of the explained variation by a linear regression model in the total variation.
Coefficient of determination
Outlier
categorical variables
Block
7. A data value that falls outside the overall pattern of the graph.
Outlier
Probability density
the population variance
Statistics
8. Is the result of applying a statistical algorithm to a data set. It can also be described as an observable random variable.
Marginal distribution
quantitative variables
Kurtosis
A statistic
9. 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
An event
Cumulative distribution functions
Sampling
Ratio measurements
10. 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
Type 2 Error
experimental studies and observational studies.
applied statistics
Interval measurements
11. 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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12. Is its expected value. The mean (or sample mean of a data set is just the average value.
experimental studies and observational studies.
Law of Parsimony
The Mean of a random variable
Marginal distribution
13. 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.
Posterior probability
A Probability measure
The median value
Treatment
14. When info. in a contingency table is re-organized into more or less categories - relationships seen can change or reverse.
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15. 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.
Experimental and observational studies
A data point
Standard error
Count data
16. 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.
Experimental and observational studies
Credence
A Statistical parameter
Descriptive
17. The collection of all possible outcomes in an experiment.
Sample space
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
observational study
Step 1 of a statistical experiment
18. 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.
A sampling distribution
Marginal probability
f(z) - and its cdf by F(z).
A data set
19. Some commonly used symbols for population parameters
the population mean
The median value
Null hypothesis
A likelihood function
20. Design of experiments - using blocking to reduce the influence of confounding variables - and randomized assignment of treatments to subjects to allow unbiased estimates of treatment effects and experimental error. At this stage - the experimenters a
Step 2 of a statistical experiment
Confounded variables
hypothesis
Conditional distribution
21. 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
Correlation coefficient
Step 3 of a statistical experiment
inferential statistics
Simpson's Paradox
22. Another name for elementary event.
Atomic event
An event
Nominal measurements
Likert scale
23. The result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data
Posterior probability
Statistical adjustment
A random variable
Simple random sample
24. S^2
descriptive statistics
s-algebras
the population variance
Inferential
25. Error also refers to the extent to which individual observations in a sample differ from a central value - such as
Conditional probability
the sample or population mean
Null hypothesis
the population cumulants
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
The sample space
Inferential statistics
Estimator
hypothesis
27. 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'
hypotheses
A data set
Conditional probability
Sampling
28. Long-term upward or downward movement over time.
The Mean of a random variable
hypotheses
Estimator
Trend
29. 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
A probability density function
Type 2 Error
Inferential statistics
Correlation
30. Planning the research - including finding the number of replicates of the study - using the following information: preliminary estimates regarding the size of treatment effects - alternative hypotheses - and the estimated experimental variability. Co
variance of X
Descriptive
Step 1 of a statistical experiment
the population correlation
31. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
Variable
hypotheses
Ordinal measurements
nominal - ordinal - interval - and ratio
32. Statistical methods can be used for summarizing or describing a collection of data; this is called
Confounded variables
methods of least squares
descriptive statistics
Type I errors
33. Var[X] :
variance of X
Independent Selection
categorical variables
Random variables
34. 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.
Conditional distribution
A statistic
A probability density function
the population mean
35. A subjective estimate of probability.
quantitative variables
Dependent Selection
Binomial experiment
Credence
36. E[X] :
Binary data
Probability density functions
expected value of X
Statistic
37. 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
Average and arithmetic mean
hypothesis
Beta value
Dependent Selection
38. Describes a characteristic of an individual to be measured or observed.
Bias
Variable
Statistical inference
Type I errors & Type II errors
39. A numerical facsimilie or representation of a real-world phenomenon.
Conditional probability
Reliable measure
Simulation
Residuals
40. (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
Law of Large Numbers
Probability density functions
The Expected value
experimental studies and observational studies.
41. The probability of correctly detecting a false null hypothesis.
Cumulative distribution functions
Power of a test
The variance of a random variable
Individual
42. 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
A probability space
nominal - ordinal - interval - and ratio
Type II errors
Probability and statistics
43. Where the null hypothesis fails to be rejected and an actual difference between populations is missed giving a 'false negative'.
That value is the median value
Binomial experiment
Pairwise independence
Type II errors
44. 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
Quantitative variable
Beta value
The standard deviation
Observational study
45. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
Probability and statistics
Binomial experiment
P-value
the population variance
46. Working from a null hypothesis two basic forms of error are recognized:
Descriptive
Type I errors & Type II errors
Probability and statistics
Pairwise independence
47. Used to reduce bias - this measure weights the more relevant information higher than less relevant info.
Statistical adjustment
Type I errors & Type II errors
nominal - ordinal - interval - and ratio
Binary data
48. A variable that has an important effect on the response variable and the relationship among the variables in a study but is not one of the explanatory variables studied either because it is unknown or not measured.
f(z) - and its cdf by F(z).
Lurking variable
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Descriptive statistics
49. Of a group of numbers is the center point of all those number values.
A probability space
The average - or arithmetic mean
Joint probability
Statistics
50. 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).
Law of Parsimony
An event
The sample space
s-algebras
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