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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.
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. Failing to reject a false null hypothesis.
Type 2 Error
Interval measurements
Independent Selection
Coefficient of determination
2. 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).
Divide the sum by the number of values.
Type 1 Error
Likert scale
Joint probability
3. 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
Power of a test
Probability
A sample
Inferential statistics
4. (pdfs) and probability mass functions are denoted by lower case letters - e.g. f(x).
Probability density functions
Simpson's Paradox
Probability
Statistical inference
5. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.
Parameter - or 'statistical parameter'
An estimate of a parameter
A random variable
Correlation coefficient
6. A variable describes an individual by placing the individual into a category or a group.
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
An experimental study
Law of Large Numbers
Qualitative variable
7. (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
Greek letters
Trend
A likelihood function
covariance of X and Y
8. A list of individuals from which the sample is actually selected.
methods of least squares
The variance of a random variable
Sampling frame
Type I errors & Type II errors
9. A numerical measure that assesses the strength of a linear relationship between two variables.
expected value of X
Correlation coefficient
The standard deviation
Parameter - or 'statistical parameter'
10. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
Binary data
Random variables
Prior probability
descriptive statistics
11. Is the set of possible outcomes of an experiment. For example - the sample space for rolling a six-sided die will be {1 - 2 - 3 - 4 - 5 - 6}.
quantitative variables
The sample space
Skewness
Lurking variable
12. The probability of correctly detecting a false null hypothesis.
s-algebras
hypothesis
Power of a test
Treatment
13. Cov[X - Y] :
Correlation
A likelihood function
covariance of X and Y
The Range
14. A numerical measure that describes an aspect of a sample.
The sample space
inferential statistics
Statistic
A population or statistical population
15. 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
Inferential statistics
Sampling
Reliable measure
Descriptive statistics
16. Statistical methods can be used for summarizing or describing a collection of data; this is called
Particular realizations of a random variable
descriptive statistics
Interval measurements
Valid measure
17. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
Alpha value (Level of Significance)
The Covariance between two random variables X and Y - with expected values E(X) =
Step 2 of a statistical experiment
Law of Large Numbers
18. Is a parameter that indexes a family of probability distributions.
Probability and statistics
Mutual independence
applied statistics
A Statistical parameter
19. A subjective estimate of probability.
Bias
Valid measure
An Elementary event
Credence
20. 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
A sampling distribution
Mutual independence
the population correlation
Bias
21. Working from a null hypothesis two basic forms of error are recognized:
An event
Type I errors & Type II errors
Observational study
Sampling Distribution
22. 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.
A probability density function
Bias
Probability
Individual
23. E[X] :
Probability density functions
expected value of X
A data point
Independent Selection
24. A scale that represents an ordinal scale such as looks on a scale from 1 to 10.
Coefficient of determination
Step 2 of a statistical experiment
P-value
Likert scale
25. 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.
A population or statistical population
Statistical inference
A random variable
Statistical dispersion
26. 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
Statistics
Statistical inference
expected value of X
hypotheses
27. Where the null hypothesis fails to be rejected and an actual difference between populations is missed giving a 'false negative'.
Power of a test
Type II errors
Quantitative variable
A population or statistical population
28. Are simply two different terms for the same thing. Add the given values
the population correlation
Interval measurements
A Distribution function
Average and arithmetic mean
29. A consistent - repeated deviation of the sample statistic from the population parameter in the same direction when many samples are taken.
Bias
The Mean of a random variable
Observational study
Beta value
30. Long-term upward or downward movement over time.
Variability
Trend
the population cumulants
The average - or arithmetic mean
31. Data are gathered and correlations between predictors and response are investigated.
experimental studies and observational studies.
s-algebras
observational study
That is the median value
32. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
covariance of X and Y
nominal - ordinal - interval - and ratio
The median value
Sample space
33. 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
inferential statistics
Skewness
Outlier
34. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
Credence
Statistical dispersion
P-value
Type II errors
35. ?r
the population cumulants
A population or statistical population
P-value
An estimate of a parameter
36. A numerical facsimilie or representation of a real-world phenomenon.
Independence or Statistical independence
Dependent Selection
Simulation
the population mean
37. 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.
A sampling distribution
Conditional distribution
the population variance
That value is the median value
38. Rejecting a true null hypothesis.
Type 1 Error
The standard deviation
An event
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
39. Is that part of a population which is actually observed.
A random variable
A sample
An Elementary event
Probability density
40. Have imprecise differences between consecutive values - but have a meaningful order to those values
hypotheses
Ordinal measurements
A data point
Outlier
41. Are written in corresponding lower case letters. For example x1 - x2 - ... - xn could be a sample corresponding to the random variable X.
The sample space
Particular realizations of a random variable
Block
Type I errors
42. Is its expected value. The mean (or sample mean of a data set is just the average value.
Posterior probability
Power of a test
Conditional probability
The Mean of a random variable
43. 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
Statistical inference
Treatment
An estimate of a parameter
experimental studies and observational studies.
44. 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
Step 3 of a statistical experiment
Dependent Selection
Cumulative distribution functions
Type II errors
45. 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'
Correlation coefficient
An event
Lurking variable
Conditional probability
46. (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 Range
s-algebras
The median value
47. Have no meaningful rank order among values.
Type 2 Error
Greek letters
A Distribution function
Nominal measurements
48. Var[X] :
Residuals
Independent Selection
variance of X
Parameter
49. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
Sampling Distribution
Power of a test
the sample or population mean
hypotheses
50. 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.
Variability
the population cumulants
Estimator
Probability