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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. Are usually written in upper case roman letters: X - Y - etc.
Correlation
Coefficient of determination
Random variables
The sample space
2. 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.
Simulation
Credence
Placebo effect
A random variable
3. A variable has a value or numerical measurement for which operations such as addition or averaging make sense.
Placebo effect
Coefficient of determination
observational study
Quantitative variable
4. 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.
Statistical adjustment
Simple random sample
A sample
nominal - ordinal - interval - and ratio
5. Var[X] :
variance of X
Atomic event
Coefficient of determination
quantitative variables
6. 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
Probability
Independence or Statistical independence
Outlier
Joint probability
7. Occurs when a subject receives no treatment - but (incorrectly) believes he or she is in fact receiving treatment and responds favorably.
An Elementary event
Type 1 Error
Placebo effect
Step 2 of a statistical experiment
8. (cdfs) are denoted by upper case letters - e.g. F(x).
That is the median value
Cumulative distribution functions
A likelihood function
Probability and statistics
9. 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
Conditional probability
Conditional distribution
Variability
10. (e.g. ? - b) are commonly used to denote unknown parameters (population parameters).
Greek letters
Cumulative distribution functions
A sampling distribution
the population mean
11. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.
Nominal measurements
An estimate of a parameter
Statistical inference
Probability density
12. A numerical facsimilie or representation of a real-world phenomenon.
Simulation
Beta value
A random variable
Sampling
13. Failing to reject a false null hypothesis.
methods of least squares
A statistic
The sample space
Type 2 Error
14. 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.
15. Describes the spread in the values of the sample statistic when many samples are taken.
Standard error
A probability space
Variability
Simple random sample
16. Is defined as the expected value of random variable (X -
A sampling distribution
descriptive statistics
Statistical dispersion
The Covariance between two random variables X and Y - with expected values E(X) =
17. Is inference about a population from a random sample drawn from it or - more generally - about a random process from its observed behavior during a finite period of time.
Statistical inference
Probability density functions
Marginal distribution
Null hypothesis
18. 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
The Expected value
Type 1 Error
That value is the median value
Step 2 of a statistical experiment
19. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
Marginal probability
Type I errors & Type II errors
nominal - ordinal - interval - and ratio
Power of a test
20. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
the population mean
Kurtosis
Law of Large Numbers
A probability space
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
Ratio measurements
Statistic
covariance of X and Y
Probability density functions
22. When there is an even number of values...
Null hypothesis
Inferential statistics
That is the median value
A Random vector
23. (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.
The sample space
Marginal probability
Sample space
An Elementary event
24. Are simply two different terms for the same thing. Add the given values
An event
Descriptive statistics
Average and arithmetic mean
Variability
25. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively
Residuals
Block
A probability space
Nominal measurements
26. 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 arithmetic mean of a set of numbers x1 - x2 - ... - xn
Probability
Step 1 of a statistical experiment
Mutual independence
27. A variable describes an individual by placing the individual into a category or a group.
Type I errors & Type II errors
A likelihood function
Inferential statistics
Qualitative variable
28. 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.
s-algebras
Joint probability
the population variance
Independent Selection
29. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
hypothesis
Probability
Sampling Distribution
The Range
30. 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.
Residuals
the sample or population mean
A sample
Conditional distribution
31. Some commonly used symbols for sample statistics
Outlier
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
A population or statistical population
Law of Large Numbers
32. Have imprecise differences between consecutive values - but have a meaningful order to those values
Divide the sum by the number of values.
The Expected value
the sample or population mean
Ordinal measurements
33. Consists of a number of independent trials repeated under identical conditions. On each trial - there are two possible outcomes.
An experimental study
Particular realizations of a random variable
The average - or arithmetic mean
Binomial experiment
34. 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.
Statistic
Statistics
A random variable
Quantitative variable
35. 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
Lurking variable
experimental studies and observational studies.
Average and arithmetic mean
Treatment
36. Describes a characteristic of an individual to be measured or observed.
Particular realizations of a random variable
Variable
Descriptive statistics
That is the median value
37. 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.
Conditional distribution
Divide the sum by the number of values.
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Estimator
38. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.
The Mean of a random variable
The Range
Descriptive
Valid measure
39. 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
nominal - ordinal - interval - and ratio
Correlation
Variable
observational study
40. Is a sample space over which a probability measure has been defined.
A probability space
Marginal probability
Marginal distribution
A likelihood function
41. Is a function that gives the probability of all elements in a given space: see List of probability distributions
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
A probability distribution
Average and arithmetic mean
A probability space
42. A numerical measure that assesses the strength of a linear relationship between two variables.
A probability density function
A sampling distribution
The standard deviation
Correlation coefficient
43. Statistical methods can be used for summarizing or describing a collection of data; this is called
descriptive statistics
Inferential statistics
Step 1 of a statistical experiment
Pairwise 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
The Mean of a random variable
Bias
Independence or Statistical independence
methods of least squares
45. 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.
Pairwise independence
Dependent Selection
methods of least squares
Variable
46. Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically - sometimes they are grouped together as
Simpson's Paradox
A sampling distribution
categorical variables
A Random vector
47. 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)
Interval measurements
Binary data
Conditional probability
the population cumulants
48. Is a process of selecting observations to obtain knowledge about a population. There are many methods to choose on which sample to do the observations.
Sampling
A sampling distribution
A statistic
A Probability measure
49. A measurement such that the random error is small
Count data
Reliable measure
Binomial experiment
Law of Parsimony
50. Interpretation of statistical information in that the assumption is that whatever is proposed as a cause has no effect on the variable being measured can often involve the development of a
Lurking variable
Null hypothesis
A sample
Statistic