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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. The objects described by a set of data: person (animal) - place - and - thing. (SUBJECTS)
Simple random sample
Individual
Inferential statistics
Quantitative variable
2. A numerical measure that describes an aspect of a population.
Step 3 of a statistical experiment
Experimental and observational studies
Parameter
expected value of X
3. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
Probability density
the population variance
Bias
Sampling Distribution
4. Given two random variables X and Y - the joint distribution of X and Y is the probability distribution of X and Y together.
Binary data
Joint distribution
Step 3 of a statistical experiment
applied statistics
5. Is a sample space over which a probability measure has been defined.
observational study
A probability space
Pairwise independence
Correlation coefficient
6. In particular - the pdf of the standard normal distribution is denoted by
Observational study
Parameter
f(z) - and its cdf by F(z).
observational study
7.
A sample
Mutual independence
Individual
the population mean
8. Of a group of numbers is the center point of all those number values.
A data set
The average - or arithmetic mean
Type II errors
Simulation
9. Many statistical methods seek to minimize the mean-squared error - and these are called
Seasonal effect
f(z) - and its cdf by F(z).
methods of least squares
Binomial experiment
10. 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
Credence
An Elementary event
Step 1 of a statistical experiment
Type I errors
11. 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
Credence
Ordinal measurements
Probability and statistics
experimental studies and observational studies.
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
Residuals
Probability
the population cumulants
Experimental and observational studies
13. Error also refers to the extent to which individual observations in a sample differ from a central value - such as
Greek letters
Probability
the sample or population mean
Parameter - or 'statistical parameter'
14. 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.
Simpson's Paradox
Sample space
Experimental and observational studies
A statistic
15. A variable describes an individual by placing the individual into a category or a group.
Dependent Selection
the population mean
Qualitative variable
Conditional probability
16. Gives the probability distribution for a continuous random variable.
That is the median value
the population mean
A probability density function
s-algebras
17. Failing to reject a false null hypothesis.
Type I errors & Type II errors
Type 2 Error
P-value
the population correlation
18. 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.
A random variable
A Random vector
Dependent Selection
Alpha value (Level of Significance)
19. Probability of rejecting a true null hypothesis.
Alpha value (Level of Significance)
Placebo effect
A Statistical parameter
Independent Selection
20. 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.
Coefficient of determination
Statistic
Kurtosis
A Probability measure
21. A measurement such that the random error is small
Variability
Reliable measure
Inferential
Nominal measurements
22. (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
Independent Selection
A Statistical parameter
Type 1 Error
23. 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
Placebo effect
A Statistical parameter
Step 2 of a statistical experiment
Coefficient of determination
24. Var[X] :
A data set
variance of X
Descriptive
Probability
25. Probability of accepting a false null hypothesis.
Beta value
Bias
inferential statistics
The Range
26. The result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data
the population mean
Statistics
Posterior probability
the population correlation
27. A scale that represents an ordinal scale such as looks on a scale from 1 to 10.
Ratio measurements
Likert scale
Statistic
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
28. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively
Greek letters
Step 1 of a statistical experiment
Statistical inference
Residuals
29. 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).
Lurking variable
Joint probability
An estimate of a parameter
Marginal distribution
30. (cdfs) are denoted by upper case letters - e.g. F(x).
Sampling
Cumulative distribution functions
applied statistics
Probability density functions
31. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
That value is the median value
Law of Large Numbers
s-algebras
A probability space
32. 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.
An experimental study
Reliable measure
Experimental and observational studies
Treatment
33. 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)
The Range
Treatment
A likelihood function
Interval measurements
34. Occurs when a subject receives no treatment - but (incorrectly) believes he or she is in fact receiving treatment and responds favorably.
Placebo effect
hypothesis
That value is the median value
A data point
35. 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.
Ordinal measurements
The Mean of a random variable
That value is the median value
Dependent Selection
36. S^2
Bias
the population variance
observational study
Sampling Distribution
37. 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.
Beta value
Particular realizations of a random variable
A data point
Qualitative variable
38. Any specific experimental condition applied to the subjects
Ordinal measurements
A sample
Treatment
Law of Large Numbers
39. When you have two or more competing models - choose the simpler of the two models.
Bias
The standard deviation
Law of Parsimony
Placebo effect
40. A numerical facsimilie or representation of a real-world phenomenon.
Statistical dispersion
That is the median value
Law of Large Numbers
Simulation
41. 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
experimental studies and observational studies.
That value is the median value
the population correlation
A sampling distribution
42. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
Simple random sample
Pairwise independence
hypotheses
Probability and statistics
43. 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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44. 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
applied statistics
Variability
45. Are usually written in upper case roman letters: X - Y - etc.
Random variables
Likert scale
The standard deviation
Ratio measurements
46. The collection of all possible outcomes in an experiment.
Sample space
Binary data
Simulation
A probability space
47. Have no meaningful rank order among values.
Posterior probability
Conditional distribution
Nominal measurements
observational study
48. ?
the population correlation
Type I errors & Type II errors
Alpha value (Level of Significance)
Individual
49. Data are gathered and correlations between predictors and response are investigated.
observational study
Law of Parsimony
s-algebras
A data point
50. A data value that falls outside the overall pattern of the graph.
Probability
Reliable measure
Greek letters
Outlier