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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. In number theory - scatter plots of data generated by a distribution function may be transformed with familiar tools used in statistics to reveal underlying patterns - which may then lead to
hypotheses
categorical variables
Block
Joint probability
2. 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.
the population variance
Probability
Dependent Selection
the sample or population mean
3. A numerical facsimilie or representation of a real-world phenomenon.
Quantitative variable
observational study
Lurking variable
Simulation
4. (or multivariate random variable) is a vector whose components are random variables on the same probability space.
methods of least squares
Coefficient of determination
A probability density function
A Random vector
5. Is data that can take only two values - usually represented by 0 and 1.
Dependent Selection
Binary data
Probability
A Random vector
6. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
Prior probability
A population or statistical population
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
The variance of a random variable
7. A measurement such that the random error is small
nominal - ordinal - interval - and ratio
Simulation
Reliable measure
Sampling Distribution
8. Describes a characteristic of an individual to be measured or observed.
An Elementary event
Treatment
Variable
Sampling
9. Any specific experimental condition applied to the subjects
the sample or population mean
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Treatment
hypotheses
10. 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
Experimental and observational studies
Probability density
A probability distribution
covariance of X and Y
11. A numerical measure that assesses the strength of a linear relationship between two variables.
An experimental study
The Covariance between two random variables X and Y - with expected values E(X) =
Treatment
Correlation coefficient
12. A measure that is relevant or appropriate as a representation of that property.
A likelihood function
experimental studies and observational studies.
Valid measure
Type II errors
13. Statistics involve methods of using information from a sample to draw conclusions regarding the population.
Average and arithmetic mean
Joint distribution
Sample space
Inferential
14. The collection of all possible outcomes in an experiment.
Residuals
methods of least squares
Sample space
Power of a test
15. Var[X] :
Reliable measure
variance of X
A data set
Probability and statistics
16. The result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data
Posterior probability
A data point
An event
Interval measurements
17. 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
Trend
Null hypothesis
An Elementary event
Random variables
18. 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.
Law of Large Numbers
Null hypothesis
The median value
Interval measurements
19. 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
Variability
Cumulative distribution functions
Nominal measurements
20. 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
Individual
variance of X
Dependent Selection
Skewness
21. 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
Seasonal effect
Law of Large Numbers
Probability
A probability space
22. 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).
Statistical dispersion
Divide the sum by the number of values.
An event
The Range
23. To find the average - or arithmetic mean - of a set of numbers:
Inferential
Posterior probability
Divide the sum by the number of values.
observational study
24. Can refer either to a sample not being representative of the population - or to the difference between the expected value of an estimator and the true value.
Bias
Atomic event
Conditional distribution
Ratio measurements
25. ?
variance of X
the population correlation
Individual
Correlation
26. (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
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
P-value
The Expected value
The standard deviation
27. 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.
A data set
Binary data
Marginal distribution
experimental studies and observational studies.
28. 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
An event
Probability
Independence or Statistical independence
Individual
29. Occurs when a subject receives no treatment - but (incorrectly) believes he or she is in fact receiving treatment and responds favorably.
Probability density functions
Binomial experiment
Sampling frame
Placebo effect
30. Failing to reject a false null hypothesis.
A population or statistical population
Conditional probability
Type 2 Error
Lurking variable
31. 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.
Statistics
Type 1 Error
Kurtosis
Sampling
32. 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.
Bias
variance of X
Qualitative variable
That value is the median value
33. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
Simulation
Binomial experiment
P-value
Parameter
34. A numerical measure that describes an aspect of a sample.
descriptive statistics
Skewness
observational study
Statistic
35. 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
An event
Ratio measurements
Simple random sample
Observational study
36. 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.
quantitative variables
Experimental and observational studies
Type II errors
applied statistics
37. Is that part of a population which is actually observed.
The Range
A sample
Law of Parsimony
A data point
38. Is defined as the expected value of random variable (X -
Marginal distribution
Standard error
The Covariance between two random variables X and Y - with expected values E(X) =
Correlation coefficient
39. Descriptive statistics and inferential statistics (a.k.a. - predictive statistics) together comprise
An Elementary event
Quantitative variable
applied statistics
Block
40. 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
hypothesis
Skewness
A data set
41. 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
hypothesis
methods of least squares
P-value
Simulation
42. Changes over time that show a regular periodicity in the data where regular means over a fixed interval; the time between repetitions is called the period.
Probability
Seasonal effect
Block
categorical variables
43. Are written in corresponding lower case letters. For example x1 - x2 - ... - xn could be a sample corresponding to the random variable X.
Posterior probability
Statistical adjustment
Particular realizations of a random variable
categorical variables
44. Another name for elementary event.
Parameter - or 'statistical parameter'
Posterior probability
inferential statistics
Atomic event
45. A variable describes an individual by placing the individual into a category or a group.
Qualitative variable
Null hypothesis
Bias
Kurtosis
46. Used to reduce bias - this measure weights the more relevant information higher than less relevant info.
An estimate of a parameter
Statistical adjustment
Joint probability
Confounded variables
47. Is the length of the smallest interval which contains all the data.
Alpha value (Level of Significance)
Probability density functions
Pairwise independence
The Range
48. 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
Probability and statistics
Step 2 of a statistical experiment
Dependent Selection
the population mean
49. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
hypotheses
Pairwise independence
The average - or arithmetic mean
Valid measure
50. Where the null hypothesis is falsely rejected giving a 'false positive'.
A random variable
Type I errors
s-algebras
Marginal probability