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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. Describes the spread in the values of the sample statistic when many samples are taken.
Variability
Sample space
The Covariance between two random variables X and Y - with expected values E(X) =
Block
2. 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
Simpson's Paradox
the population variance
quantitative variables
3. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
nominal - ordinal - interval - and ratio
The Expected value
Null hypothesis
Confounded variables
4. (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
An event
The Expected value
Likert scale
Average and arithmetic mean
5. Is a function that gives the probability of all elements in a given space: see List of probability distributions
A data set
Statistical inference
Correlation
A probability distribution
6. 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.
Marginal distribution
Correlation
Skewness
Simple random sample
7. Are written in corresponding lower case letters. For example x1 - x2 - ... - xn could be a sample corresponding to the random variable X.
Interval measurements
Particular realizations of a random variable
categorical variables
Correlation coefficient
8. 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.
quantitative variables
Binary data
Dependent Selection
Bias
9. Is defined as the expected value of random variable (X -
The Covariance between two random variables X and Y - with expected values E(X) =
hypothesis
Statistical inference
Dependent Selection
10. 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.
The median value
the population cumulants
methods of least squares
the population correlation
11. Ratio and interval measurements which can be either discrete or continuous - due to their numerical nature are grouped together as
quantitative variables
The standard deviation
Average and arithmetic mean
P-value
12. 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
Statistical adjustment
Statistic
variance of X
Probability
13. 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
A Distribution function
Type I errors & Type II errors
A Statistical parameter
14. E[X] :
Individual
the sample or population mean
expected value of X
Correlation
15. 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.
methods of least squares
Conditional distribution
experimental studies and observational studies.
Statistical inference
16. Where the null hypothesis fails to be rejected and an actual difference between populations is missed giving a 'false negative'.
inferential statistics
An estimate of a parameter
Type II errors
the population variance
17. Working from a null hypothesis two basic forms of error are recognized:
Binomial experiment
Likert scale
experimental studies and observational studies.
Type I errors & Type II errors
18. Is a measure of the 'peakedness' of the probability distribution of a real-valued random variable. Higher kurtosis means more of the variance is due to infrequent extreme deviations - as opposed to frequent modestly sized deviations.
s-algebras
Kurtosis
Inferential statistics
Simulation
19. S^2
Step 2 of a statistical experiment
Parameter - or 'statistical parameter'
the population variance
Binomial experiment
20. (e.g. ? - b) are commonly used to denote unknown parameters (population parameters).
Statistic
Greek letters
Correlation coefficient
observational study
21. 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
The Covariance between two random variables X and Y - with expected values E(X) =
the population mean
Alpha value (Level of Significance)
Step 1 of a statistical experiment
22. 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.
A data point
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
A Distribution function
The average - or arithmetic mean
23. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
Law of Large Numbers
A Statistical parameter
s-algebras
Statistical adjustment
24. Is the most commonly used measure of statistical dispersion. It is the square root of the variance - and is generally written s (sigma).
The standard deviation
categorical variables
The Mean of a random variable
Type II errors
25. 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}.
Statistical inference
Likert scale
Parameter - or 'statistical parameter'
The sample space
26. 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.
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
A Probability measure
An experimental study
Correlation coefficient
27. (pdfs) and probability mass functions are denoted by lower case letters - e.g. f(x).
Probability density functions
Average and arithmetic mean
quantitative variables
Parameter - or 'statistical parameter'
28. When info. in a contingency table is re-organized into more or less categories - relationships seen can change or reverse.
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29. 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.
the population variance
Treatment
descriptive statistics
Independent Selection
30. 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
Experimental and observational studies
Mutual independence
Joint probability
observational study
31. 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'
Nominal measurements
Conditional probability
Inferential
Null hypothesis
32. 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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33. A numerical facsimilie or representation of a real-world phenomenon.
Simulation
A data set
Bias
Cumulative distribution functions
34. Is the result of applying a statistical algorithm to a data set. It can also be described as an observable random variable.
Random variables
That is the median value
Atomic event
A statistic
35. 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.
Random variables
Independence or Statistical independence
Marginal probability
Type 2 Error
36. 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.
Variability
A data point
Conditional probability
A Statistical parameter
37. 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 probability distribution
categorical variables
Interval measurements
A Distribution function
38. Is the probability distribution - under repeated sampling of the population - of a given statistic.
A sampling distribution
the population cumulants
Mutual independence
the population variance
39. When you have two or more competing models - choose the simpler of the two models.
Bias
A Distribution function
Variable
Law of Parsimony
40. Probability of rejecting a true null hypothesis.
Alpha value (Level of Significance)
Probability density
Experimental and observational studies
Coefficient of determination
41. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
Law of Large Numbers
Statistical dispersion
observational study
Prior probability
42. Descriptive statistics and inferential statistics (a.k.a. - predictive statistics) together comprise
applied statistics
Skewness
A random variable
methods of least squares
43. 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
A data point
Simulation
Lurking variable
Descriptive statistics
44. Another name for elementary event.
Atomic event
The Covariance between two random variables X and Y - with expected values E(X) =
Reliable measure
A Statistical parameter
45. Data are gathered and correlations between predictors and response are investigated.
A data point
The Range
An Elementary event
observational study
46.
Dependent Selection
the population mean
Parameter
Alpha value (Level of Significance)
47. A group of individuals sharing some common features that might affect the treatment.
quantitative variables
Block
Beta value
That is the median value
48. A scale that represents an ordinal scale such as looks on a scale from 1 to 10.
descriptive statistics
Probability
Marginal probability
Likert scale
49. Two variables such that their effects on the response variable cannot be distinguished from each other.
An experimental study
Confounded variables
Greek letters
Simpson's Paradox
50. The objects described by a set of data: person (animal) - place - and - thing. (SUBJECTS)
Divide the sum by the number of values.
A data set
Individual
Credence