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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.
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. To find the median value of a set of numbers: Arrange the numbers in numerical order. Locate the two middle numbers in the list. Find the average of those two middle values.
Correlation coefficient
Trend
That value is the median value
An Elementary event
2. The collection of all possible outcomes in an experiment.
A Distribution function
Independent Selection
Sample space
Conditional probability
3. In particular - the pdf of the standard normal distribution is denoted by
f(z) - and its cdf by F(z).
Confounded variables
Law of Large Numbers
Sampling Distribution
4. Another name for elementary event.
Atomic event
Greek letters
The median value
Conditional probability
5. 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
The variance of a random variable
Statistic
Mutual independence
hypothesis
6. Probability of rejecting a true null hypothesis.
Alpha value (Level of Significance)
Independence or Statistical independence
Quantitative variable
covariance of X and Y
7. Failing to reject a false null hypothesis.
Step 3 of a statistical experiment
Simple random sample
Outlier
Type 2 Error
8. Is used in 'mathematical statistics' (alternatively - 'statistical theory') to study the sampling distributions of sample statistics and - more generally - the properties of statistical procedures. The use of any statistical method is valid when the
Marginal distribution
An Elementary event
The Range
Probability
9. 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.
Type 1 Error
Simple random sample
Statistical dispersion
Descriptive
10. Have imprecise differences between consecutive values - but have a meaningful order to those values
Estimator
Random variables
quantitative variables
Ordinal measurements
11. Statistical methods can be used for summarizing or describing a collection of data; this is called
Probability density
descriptive statistics
Reliable measure
Type II errors
12. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.
Joint distribution
Average and arithmetic mean
Descriptive
methods of least squares
13. 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.
The average - or arithmetic mean
Greek letters
Marginal distribution
Nominal measurements
14. A consistent - repeated deviation of the sample statistic from the population parameter in the same direction when many samples are taken.
A probability density function
Bias
Law of Parsimony
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
15. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
P-value
Marginal probability
Treatment
Bias
16. Is a sample and the associated data points.
Binary data
Correlation coefficient
The average - or arithmetic mean
A data set
17. 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
Reliable measure
Random variables
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Observational study
18. (e.g. ? - b) are commonly used to denote unknown parameters (population parameters).
Statistic
covariance of X and Y
Greek letters
P-value
19. A group of individuals sharing some common features that might affect the treatment.
Parameter - or 'statistical parameter'
Independence or Statistical independence
A Random vector
Block
20. Is a parameter that indexes a family of probability distributions.
observational study
A Distribution function
A Statistical parameter
Likert scale
21. 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
Qualitative variable
Ratio measurements
methods of least squares
22. 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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23. A numerical measure that describes an aspect of a population.
A Distribution function
Descriptive statistics
Parameter
Parameter - or 'statistical parameter'
24. Are usually written in upper case roman letters: X - Y - etc.
Random variables
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Type 2 Error
Treatment
25. 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
Null hypothesis
Binomial experiment
Statistical adjustment
26. The objects described by a set of data: person (animal) - place - and - thing. (SUBJECTS)
Residuals
Null hypothesis
Descriptive statistics
Individual
27. ?r
Coefficient of determination
Pairwise independence
An Elementary event
the population cumulants
28. A variable has a value or numerical measurement for which operations such as addition or averaging make sense.
The sample space
Conditional distribution
Atomic event
Quantitative variable
29. Is defined as the expected value of random variable (X -
Statistical adjustment
The Covariance between two random variables X and Y - with expected values E(X) =
Observational study
An event
30. Statistics involve methods of using information from a sample to draw conclusions regarding the population.
Correlation coefficient
Inferential
That is the median value
The Expected value
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.
A Statistical parameter
Confounded variables
A data point
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
32. 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.
Quantitative variable
Estimator
Random variables
Sampling
33. Describes the spread in the values of the sample statistic when many samples are taken.
Independent Selection
Variability
Parameter
Probability density
34. Ratio and interval measurements which can be either discrete or continuous - due to their numerical nature are grouped together as
quantitative variables
A Probability measure
Marginal probability
Individual
35. The result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data
Ratio measurements
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Posterior probability
Descriptive
36. (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
A probability density function
A sample
Probability density
37. 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.
Confounded variables
Lurking variable
Individual
Statistic
38. 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.
hypothesis
Dependent Selection
methods of least squares
expected value of X
39. 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
Law of Large Numbers
Step 3 of a statistical experiment
Individual
Parameter - or 'statistical parameter'
40. Some commonly used symbols for sample statistics
Treatment
Type I errors & Type II errors
Probability density
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
41. A list of individuals from which the sample is actually selected.
Step 1 of a statistical experiment
Sampling frame
Nominal measurements
Simulation
42. Probability of accepting a false null hypothesis.
experimental studies and observational studies.
methods of least squares
Type I errors
Beta value
43. 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).
Simple random sample
An event
The median value
Independence or Statistical independence
44. 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
Probability and statistics
Independence or Statistical independence
Qualitative variable
Confounded variables
45. 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.
Correlation
Independent Selection
Descriptive
Confounded variables
46. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively
Residuals
the population mean
Probability and statistics
Step 3 of a statistical experiment
47. 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.
the sample or population mean
A Distribution function
Step 1 of a statistical experiment
Statistics
48. 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
the population mean
Beta value
Alpha value (Level of Significance)
49. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.
Ordinal measurements
A probability density function
s-algebras
An estimate of a parameter
50. Some commonly used symbols for population parameters
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Likert scale
the population mean
Correlation coefficient
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