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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. 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
Interval measurements
Independent Selection
Parameter
2. Ratio and interval measurements which can be either discrete or continuous - due to their numerical nature are grouped together as
quantitative variables
A population or statistical population
Divide the sum by the number of values.
A sampling distribution
3. A variable has a value or numerical measurement for which operations such as addition or averaging make sense.
Quantitative variable
A Statistical parameter
Random variables
Descriptive statistics
4. Is the probability distribution - under repeated sampling of the population - of a given statistic.
the population mean
A sampling distribution
the population variance
Joint distribution
5. 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
A probability distribution
Null hypothesis
A Statistical parameter
Simple random sample
6. Is defined as the expected value of random variable (X -
Count data
The Expected value
Marginal distribution
The Covariance between two random variables X and Y - with expected values E(X) =
7. 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
Step 2 of a statistical experiment
P-value
That is the median value
Binary data
8. Describes a characteristic of an individual to be measured or observed.
Valid measure
Variable
Treatment
the population cumulants
9. 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.
hypotheses
Simulation
That value is the median value
Confounded variables
10. The proportion of the explained variation by a linear regression model in the total variation.
Coefficient of determination
Step 2 of a statistical experiment
Block
Bias
11. Statistical methods can be used for summarizing or describing a collection of data; this is called
Nominal measurements
Joint distribution
descriptive statistics
Step 1 of a statistical experiment
12. A measure that is relevant or appropriate as a representation of that property.
Placebo effect
Binomial experiment
The standard deviation
Valid measure
13. Is a parameter that indexes a family of probability distributions.
variance of X
A Statistical parameter
Seasonal effect
Particular realizations of a random variable
14. 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
experimental studies and observational studies.
variance of X
Type II errors
Mutual independence
15. Of a group of numbers is the center point of all those number values.
The average - or arithmetic mean
Atomic event
Kurtosis
Likert scale
16. Probability of accepting a false null hypothesis.
A random variable
Law of Parsimony
Correlation coefficient
Beta value
17. 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
s-algebras
Ratio measurements
Statistics
Law of Large Numbers
18. Descriptive statistics and inferential statistics (a.k.a. - predictive statistics) together comprise
Observational study
Type 2 Error
applied statistics
Probability density functions
19. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively
Variability
Residuals
Experimental and observational studies
Simpson's Paradox
20. Error also refers to the extent to which individual observations in a sample differ from a central value - such as
A data point
hypotheses
Divide the sum by the number of values.
the sample or population mean
21. Are usually written with upper case calligraphic (e.g. F for the set of sets on which we define the probability P)
s-algebras
Individual
hypotheses
A data point
22. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
Experimental and observational studies
Law of Large Numbers
Inferential statistics
P-value
23. Is the probability of an event - ignoring any information about other events. The marginal probability of A is written P(A). Contrast with conditional probability.
Count data
Simulation
Marginal probability
Statistical inference
24. Working from a null hypothesis two basic forms of error are recognized:
Type I errors & Type II errors
Valid measure
Variable
Outlier
25. 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
Skewness
expected value of X
Marginal distribution
Trend
26. Some commonly used symbols for population parameters
The sample space
Ratio measurements
quantitative variables
the population mean
27. Gives the probability distribution for a continuous random variable.
A probability density function
Step 1 of a statistical experiment
Valid measure
Bias
28. A numerical measure that assesses the strength of a linear relationship between two variables.
hypotheses
Correlation coefficient
Law of Parsimony
applied statistics
29. (e.g. ? - b) are commonly used to denote unknown parameters (population parameters).
Seasonal effect
Greek letters
Step 3 of a statistical experiment
Block
30. Var[X] :
Divide the sum by the number of values.
variance of X
Descriptive
Count data
31. 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
A sampling distribution
Binary data
Correlation
Qualitative variable
32.
Power of a test
the population mean
Simulation
Inferential statistics
33. The collection of all possible outcomes in an experiment.
Interval measurements
Sample space
Descriptive statistics
A sampling distribution
34. Have no meaningful rank order among values.
the population cumulants
Descriptive
Nominal measurements
A likelihood function
35. 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.
A data set
A population or statistical population
Probability
An Elementary event
36. Is denoted by - pronounced 'x bar'.
quantitative variables
Probability density
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
the sample or population mean
37. 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
Inferential statistics
Joint distribution
covariance of X and Y
Statistical dispersion
38. 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
A Probability measure
Kurtosis
Marginal probability
39. Are written in corresponding lower case letters. For example x1 - x2 - ... - xn could be a sample corresponding to the random variable X.
Cumulative distribution functions
An Elementary event
Particular realizations of a random variable
inferential statistics
40. Failing to reject a false null hypothesis.
Type 2 Error
Seasonal effect
Probability
The Range
41. Have imprecise differences between consecutive values - but have a meaningful order to those values
Beta value
the population mean
Ordinal measurements
A likelihood function
42. Are two related but separate academic disciplines. Statistical analysis often uses probability distributions - and the two topics are often studied together. However - probability theory contains much that is of mostly of mathematical interest and no
Block
Bias
Lurking variable
Probability and statistics
43. Is a function that gives the probability of all elements in a given space: see List of probability distributions
Placebo effect
A probability distribution
Probability
The Mean of a random variable
44. 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
Reliable measure
inferential statistics
Step 1 of a statistical experiment
Ratio measurements
45. 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
Reliable measure
f(z) - and its cdf by F(z).
Descriptive statistics
Residuals
46. 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
A Random vector
Type 2 Error
Correlation
47. Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically - sometimes they are grouped together as
Step 1 of a statistical experiment
Valid measure
categorical variables
inferential statistics
48. 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.
the population correlation
Statistical inference
Statistical adjustment
the population variance
49. 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
Type I errors & Type II errors
Type II errors
Particular realizations of a random variable
50. Where the null hypothesis fails to be rejected and an actual difference between populations is missed giving a 'false negative'.
Law of Parsimony
A likelihood function
Type II errors
Divide the sum by the number of values.