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Test your basic knowledge |
CLEP General Mathematics: Probability And Statistics
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clep
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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. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.
The standard deviation
Dependent Selection
f(z) - and its cdf by F(z).
Descriptive
2. 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.
Prior probability
Qualitative variable
Bias
Type 2 Error
3. Statistics involve methods of using information from a sample to draw conclusions regarding the population.
Law of Parsimony
The standard deviation
Divide the sum by the number of values.
Inferential
4. Is a function that gives the probability of all elements in a given space: see List of probability distributions
A sample
A probability distribution
Inferential
Residuals
5. 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.
Seasonal effect
Qualitative variable
hypothesis
Posterior probability
6. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
variance of X
Particular realizations of a random variable
Simple random sample
Law of Large Numbers
7. 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.
The standard deviation
applied statistics
Simpson's Paradox
Statistics
8. Describes a characteristic of an individual to be measured or observed.
s-algebras
An experimental study
Variable
The Expected value
9. A numerical measure that assesses the strength of a linear relationship between two variables.
the population mean
Correlation coefficient
Kurtosis
Statistical adjustment
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
Type 2 Error
the population cumulants
Probability density
Valid measure
11. 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
Pairwise independence
Skewness
inferential statistics
categorical variables
12. (also called statistical variability) is a measure of how diverse some data is. It can be expressed by the variance or the standard deviation.
Statistical dispersion
The Expected value
Step 1 of a statistical experiment
Power of a test
13. Describes the spread in the values of the sample statistic when many samples are taken.
Observational study
Beta value
Variability
The Mean of a random variable
14. Are written in corresponding lower case letters. For example x1 - x2 - ... - xn could be a sample corresponding to the random variable X.
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Particular realizations of a random variable
the population cumulants
Coefficient of determination
15. Given two random variables X and Y - the joint distribution of X and Y is the probability distribution of X and Y together.
Power of a test
Confounded variables
the population cumulants
Joint distribution
16. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
An experimental study
hypotheses
Variable
Pairwise independence
17. The proportion of the explained variation by a linear regression model in the total variation.
Probability density functions
applied statistics
Simpson's Paradox
Coefficient of determination
18. Have imprecise differences between consecutive values - but have a meaningful order to those values
Simpson's Paradox
Ordinal measurements
An estimate of a parameter
Variable
19. 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
hypothesis
Simpson's Paradox
Descriptive statistics
variance of X
20. Failing to reject a false null hypothesis.
The Covariance between two random variables X and Y - with expected values E(X) =
Joint distribution
the population mean
Type 2 Error
21. 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.
Kurtosis
Valid measure
That value is the median value
Probability density functions
22. The objects described by a set of data: person (animal) - place - and - thing. (SUBJECTS)
Individual
methods of least squares
An estimate of a parameter
Bias
23. When info. in a contingency table is re-organized into more or less categories - relationships seen can change or reverse.
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24. 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.
Descriptive
Conditional probability
An event
Kurtosis
25. 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
Correlation
A Statistical parameter
Trend
covariance of X and Y
26. 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.
Interval measurements
Type I errors & Type II errors
Posterior probability
A data point
27. Is the length of the smallest interval which contains all the data.
f(z) - and its cdf by F(z).
Probability and statistics
The Range
Residuals
28. The collection of all possible outcomes in an experiment.
Sample space
Statistical inference
Parameter - or 'statistical parameter'
Greek letters
29. A data value that falls outside the overall pattern of the graph.
Outlier
Step 1 of a statistical experiment
That value is the median value
Average and arithmetic mean
30. 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
Outlier
Null hypothesis
Sampling frame
hypothesis
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'
Qualitative variable
Binary data
inferential statistics
Conditional probability
32. 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.
Descriptive
Power of a test
Probability density
A random variable
33. (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
Prior probability
A random variable
Estimator
34. (e.g. ? - b) are commonly used to denote unknown parameters (population parameters).
Inferential statistics
Greek letters
Marginal distribution
Sample space
35. (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.
An Elementary event
the population cumulants
the population mean
Correlation
36. 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
Particular realizations of a random variable
Quantitative variable
Type I errors & Type II errors
Probability
37. (pdfs) and probability mass functions are denoted by lower case letters - e.g. f(x).
Probability density functions
A Statistical parameter
Outlier
Dependent Selection
38. Probability of rejecting a true null hypothesis.
Residuals
Alpha value (Level of Significance)
An event
Probability and statistics
39. ?r
the population cumulants
hypotheses
Divide the sum by the number of values.
Individual
40. Data are gathered and correlations between predictors and response are investigated.
A sample
observational study
Valid measure
Sampling
41. Is data arising from counting that can take only non-negative integer values.
A sample
Count data
s-algebras
Law of Parsimony
42. Are usually written with upper case calligraphic (e.g. F for the set of sets on which we define the probability P)
s-algebras
Simulation
Parameter - or 'statistical parameter'
Binomial experiment
43. Some commonly used symbols for population parameters
The Expected value
Conditional distribution
the population mean
Descriptive statistics
44. Two variables such that their effects on the response variable cannot be distinguished from each other.
Confounded variables
Statistical adjustment
Kurtosis
Dependent Selection
45. Is data that can take only two values - usually represented by 0 and 1.
descriptive statistics
Binary data
Statistical dispersion
Atomic event
46. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively
Greek letters
Residuals
Beta value
Inferential
47. Have no meaningful rank order among values.
Descriptive statistics
Nominal measurements
Likert scale
Statistical adjustment
48. A group of individuals sharing some common features that might affect the treatment.
Nominal measurements
Standard error
Block
Independence or Statistical independence
49.
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Joint distribution
the population mean
A sampling distribution
50. Is a set of entities about which statistical inferences are to be drawn - often based on random sampling. One can also talk about a population of measurements or values.
Joint distribution
A population or statistical population
The Covariance between two random variables X and Y - with expected values E(X) =
A Random vector