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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.
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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. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
Conditional distribution
The Expected value
Simpson's Paradox
nominal - ordinal - interval - and ratio
2. Is a sample and the associated data points.
The Covariance between two random variables X and Y - with expected values E(X) =
Simulation
Interval measurements
A data set
3. A subjective estimate of probability.
Conditional distribution
An experimental study
Credence
Sampling Distribution
4. (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
Standard error
Dependent Selection
covariance of X and Y
A likelihood function
5. Are written in corresponding lower case letters. For example x1 - x2 - ... - xn could be a sample corresponding to the random variable X.
Nominal measurements
Particular realizations of a random variable
Sampling Distribution
Simple random sample
6. A measurement such that the random error is small
Reliable measure
Binomial experiment
Marginal probability
covariance of X and Y
7. 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.
Greek letters
A likelihood function
Experimental and observational studies
Joint distribution
8. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively
The Covariance between two random variables X and Y - with expected values E(X) =
Residuals
That is the median value
methods of least squares
9. 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.
P-value
variance of X
Estimator
Beta value
10. Is a parameter that indexes a family of probability distributions.
A Statistical parameter
Parameter - or 'statistical parameter'
Type 2 Error
A sample
11. Two variables such that their effects on the response variable cannot be distinguished from each other.
Conditional distribution
A probability density function
Confounded variables
Statistic
12. Where the null hypothesis is falsely rejected giving a 'false positive'.
s-algebras
Type I errors
Probability density
Simpson's Paradox
13. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
Independence or Statistical independence
Sampling frame
P-value
A Random vector
14. Consists of a number of independent trials repeated under identical conditions. On each trial - there are two possible outcomes.
Valid measure
Residuals
Quantitative variable
Binomial experiment
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.
Particular realizations of a random variable
Atomic event
Seasonal effect
Ratio measurements
16. 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}.
Variability
Cumulative distribution functions
The sample space
Experimental and observational studies
17. Many statistical methods seek to minimize the mean-squared error - and these are called
methods of least squares
Type I errors & Type II errors
Cumulative distribution functions
A data point
18. Another name for elementary event.
Binomial experiment
Simulation
A Random vector
Atomic event
19. 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
That value is the median value
observational study
Ratio measurements
The average - or arithmetic mean
20. 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
Independence or Statistical independence
Correlation coefficient
A sampling distribution
covariance of X and Y
21. Long-term upward or downward movement over time.
the sample or population mean
Trend
Ratio measurements
Probability density
22. A consistent - repeated deviation of the sample statistic from the population parameter in the same direction when many samples are taken.
Lurking variable
methods of least squares
Statistical dispersion
Bias
23. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
The variance of a random variable
Prior probability
An estimate of a parameter
Average and arithmetic mean
24. 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.
An event
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Marginal probability
Credence
25. A list of individuals from which the sample is actually selected.
hypotheses
Standard error
Lurking variable
Sampling frame
26. (e.g. ? - b) are commonly used to denote unknown parameters (population parameters).
A population or statistical population
Greek letters
Skewness
An event
27. The collection of all possible outcomes in an experiment.
f(z) - and its cdf by F(z).
Descriptive
Sample space
Confounded variables
28. ?
the population correlation
Treatment
Outlier
A sampling distribution
29. Have no meaningful rank order among values.
Simple random sample
Lurking variable
experimental studies and observational studies.
Nominal measurements
30. Can be a population parameter - a distribution parameter - an unobserved parameter (with different shades of meaning). In statistics - this is often a quantity to be estimated.
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31. A numerical measure that assesses the strength of a linear relationship between two variables.
The sample space
Correlation coefficient
Posterior probability
Bias
32. 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.
Marginal distribution
Alpha value (Level of Significance)
Nominal measurements
the population correlation
33. Gives the probability distribution for a continuous random variable.
variance of X
Treatment
Ordinal measurements
A probability density function
34. A scale that represents an ordinal scale such as looks on a scale from 1 to 10.
Likert scale
Outlier
Probability density
Coefficient of determination
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.
Type I errors
Mutual independence
Joint probability
A population or statistical population
36. 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.
Bias
A population or statistical population
An experimental study
Statistical dispersion
37. 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
Descriptive statistics
Probability density
A sample
The standard deviation
38. 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
expected value of X
Observational study
Joint probability
applied statistics
39. 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.
Skewness
categorical variables
A probability density function
The median value
40. Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically - sometimes they are grouped together as
categorical variables
Independent Selection
A sample
Conditional probability
41. 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.
Quantitative variable
the sample or population mean
Statistic
Bias
42. Are usually written with upper case calligraphic (e.g. F for the set of sets on which we define the probability P)
Block
s-algebras
variance of X
nominal - ordinal - interval - and ratio
43. 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.
Sample space
A sample
Type 1 Error
Statistics
44. Is its expected value. The mean (or sample mean of a data set is just the average value.
The Mean of a random variable
Trend
Simple random sample
Conditional probability
45. Statistical methods can be used for summarizing or describing a collection of data; this is called
descriptive statistics
Skewness
Outlier
Coefficient of determination
46. Describes the spread in the values of the sample statistic when many samples are taken.
A probability density function
quantitative variables
A data set
Variability
47. A numerical measure that describes an aspect of a population.
Seasonal effect
Statistical inference
Kurtosis
Parameter
48. 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
Conditional probability
nominal - ordinal - interval - and ratio
hypothesis
Sampling frame
49. (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.
P-value
Greek letters
An Elementary event
Standard error
50. When you have two or more competing models - choose the simpler of the two models.
Variability
Seasonal effect
Law of Parsimony
A sample
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