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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. Ratio and interval measurements which can be either discrete or continuous - due to their numerical nature are grouped together as
Divide the sum by the number of values.
quantitative variables
The variance of a random variable
Likert scale
2. Are written in corresponding lower case letters. For example x1 - x2 - ... - xn could be a sample corresponding to the random variable X.
Particular realizations of a random variable
Skewness
A Probability measure
Independent Selection
3. 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.
Posterior probability
Skewness
Statistical inference
Simple random sample
4. 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
Outlier
Descriptive
A population or statistical population
5. Statistics involve methods of using information from a sample to draw conclusions regarding the population.
variance of X
Inferential
categorical variables
Ratio measurements
6. 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
Conditional distribution
Variability
Type I errors
inferential statistics
7. 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.
Inferential
An experimental study
s-algebras
Alpha value (Level of Significance)
8. A variable describes an individual by placing the individual into a category or a group.
Qualitative variable
s-algebras
A random variable
Independence or Statistical independence
9. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.
An estimate of a parameter
Parameter
A Distribution function
variance of X
10. 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
Law of Large Numbers
The sample space
Treatment
11. 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 sampling distribution
A random variable
Descriptive
Seasonal effect
12. Have no meaningful rank order among values.
Nominal measurements
Interval measurements
Outlier
That is the median value
13. 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
Standard error
the population mean
Variable
hypotheses
14. Failing to reject a false null hypothesis.
A Distribution function
Type 2 Error
the population cumulants
Beta value
15. 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.
Atomic event
Type 2 Error
Seasonal effect
A population or statistical population
16. 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.
Lurking variable
Step 3 of a statistical experiment
Sampling
An event
17. The probability of correctly detecting a false null hypothesis.
the population cumulants
Bias
A population or statistical population
Power of a test
18. Descriptive statistics and inferential statistics (a.k.a. - predictive statistics) together comprise
Greek letters
Type 1 Error
Prior probability
applied statistics
19. The standard deviation of a sampling distribution.
methods of least squares
Sampling
Inferential statistics
Standard error
20. 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 data point
Interval measurements
Seasonal effect
Outlier
21. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
Probability
A data point
Prior probability
Marginal probability
22. Two variables such that their effects on the response variable cannot be distinguished from each other.
Greek letters
Estimator
the population variance
Confounded variables
23. Are usually written with upper case calligraphic (e.g. F for the set of sets on which we define the probability P)
Step 1 of a statistical experiment
s-algebras
Type I errors
Statistical adjustment
24. Error also refers to the extent to which individual observations in a sample differ from a central value - such as
Inferential statistics
That is the median value
categorical variables
the sample or population mean
25. A numerical measure that assesses the strength of a linear relationship between two variables.
Power of a test
f(z) - and its cdf by F(z).
Mutual independence
Correlation coefficient
26. Another name for elementary event.
Statistics
Probability density functions
Atomic event
A sample
27. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively
Interval measurements
variance of X
Residuals
Simple random sample
28. 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.
P-value
Experimental and observational studies
Statistical adjustment
Random variables
29. 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.
Lurking variable
Placebo effect
Qualitative variable
A sampling distribution
30. Data are gathered and correlations between predictors and response are investigated.
A sampling distribution
Likert scale
Simpson's Paradox
observational study
31. 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
A probability density function
Correlation
Mutual independence
32. When you have two or more competing models - choose the simpler of the two models.
Law of Parsimony
Statistical adjustment
Variability
A random variable
33. 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.
experimental studies and observational studies.
A Distribution function
A probability distribution
Experimental and observational studies
34. Is the length of the smallest interval which contains all the data.
Ordinal measurements
The variance of a random variable
The Range
Alpha value (Level of Significance)
35. Is its expected value. The mean (or sample mean of a data set is just the average value.
nominal - ordinal - interval - and ratio
The Mean of a random variable
Conditional distribution
Conditional probability
36. 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
The Expected value
A population or statistical population
Joint distribution
hypothesis
37. Is that part of a population which is actually observed.
A sample
Kurtosis
That value is the median value
Sampling Distribution
38. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
Trend
Sampling Distribution
Type 1 Error
Individual
39. Used to reduce bias - this measure weights the more relevant information higher than less relevant info.
Random variables
applied statistics
Sampling frame
Statistical adjustment
40.
the population mean
Independent Selection
Lurking variable
Independence or Statistical independence
41. A measurement such that the random error is small
Valid measure
A Distribution function
An experimental study
Reliable measure
42. Uses patterns in the sample data to draw inferences about the population represented - accounting for randomness. These inferences may take the form of: answering yes/no questions about the data (hypothesis testing) - estimating numerical characteris
Prior probability
A Distribution function
Inferential statistics
Observational study
43. A numerical measure that describes an aspect of a population.
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Parameter
categorical variables
Dependent Selection
44. Given two random variables X and Y - the joint distribution of X and Y is the probability distribution of X and Y together.
Statistical adjustment
Step 1 of a statistical experiment
Binary data
Joint distribution
45. (or multivariate random variable) is a vector whose components are random variables on the same probability space.
A Random vector
A Distribution function
Random variables
applied statistics
46. 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
categorical variables
Step 3 of a statistical experiment
Conditional probability
Dependent Selection
47. Is a measure of its statistical dispersion - indicating how far from the expected value its values typically are. The variance of random variable X is typically designated as - - or simply s2.
Beta value
The variance of a random variable
Ratio measurements
Mutual independence
48. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
Inferential
applied statistics
A probability density function
nominal - ordinal - interval - and ratio
49. Gives the probability of events in a probability space.
That is the median value
Marginal probability
The Range
A Probability measure
50. Some commonly used symbols for sample statistics
A Probability measure
Statistical dispersion
A Statistical parameter
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.