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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.
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. A numerical measure that assesses the strength of a linear relationship between two variables.
The sample space
variance of X
Correlation
Correlation coefficient
2. Samples are drawn from two different populations such that the sample data drawn from one population is completely unrelated to the selection of sample data from the other population.
Independent Selection
Step 3 of a statistical experiment
Marginal distribution
Simpson's Paradox
3. 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
Mutual independence
Probability
Statistic
That value is the median value
4. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
Inferential statistics
Parameter
Experimental and observational studies
Pairwise independence
5. 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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6. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
An event
nominal - ordinal - interval - and ratio
Skewness
Type I errors
7. 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
The sample space
The Covariance between two random variables X and Y - with expected values E(X) =
Inferential statistics
Seasonal effect
8. 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.
Descriptive
Outlier
Conditional distribution
inferential statistics
9. Many statistical methods seek to minimize the mean-squared error - and these are called
Correlation
methods of least squares
Parameter - or 'statistical parameter'
Skewness
10. Occurs when a subject receives no treatment - but (incorrectly) believes he or she is in fact receiving treatment and responds favorably.
That value is the median value
Residuals
Placebo effect
Type I errors & Type II errors
11. 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
Reliable measure
Valid measure
Statistics
12. 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
Type II errors
expected value of X
Ordinal measurements
13. A sample selected in such a way that each individual is equally likely to be selected as well as any group of size n is equally likely to be selected.
categorical variables
Simple random sample
A probability space
Block
14. Is a subset of the sample space - to which a probability can be assigned. For example - on rolling a die - 'getting a five or a six' is an event (with a probability of one third if the die is fair).
Pairwise independence
Alpha value (Level of Significance)
A Probability measure
An event
15. Gives the probability of events in a probability space.
Step 2 of a statistical experiment
A Probability measure
Inferential statistics
Step 3 of a statistical experiment
16. A consistent - repeated deviation of the sample statistic from the population parameter in the same direction when many samples are taken.
Nominal measurements
categorical variables
Observational study
Bias
17. 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.
inferential statistics
Lurking variable
Sampling
Mutual independence
18. When info. in a contingency table is re-organized into more or less categories - relationships seen can change or reverse.
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19. Planning the research - including finding the number of replicates of the study - using the following information: preliminary estimates regarding the size of treatment effects - alternative hypotheses - and the estimated experimental variability. Co
Standard error
Simple random sample
Step 1 of a statistical experiment
An estimate of a parameter
20. Is the most commonly used measure of statistical dispersion. It is the square root of the variance - and is generally written s (sigma).
categorical variables
The standard deviation
A data set
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
21. Is the probability distribution - under repeated sampling of the population - of a given statistic.
A sampling distribution
Mutual independence
The variance of a random variable
Standard error
22. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
Prior probability
Block
An Elementary event
descriptive statistics
23. Is data that can take only two values - usually represented by 0 and 1.
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Binary data
Interval measurements
Type 1 Error
24. Error also refers to the extent to which individual observations in a sample differ from a central value - such as
Marginal distribution
Bias
the sample or population mean
Inferential
25. 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
An Elementary event
Probability and statistics
Variable
Probability density
26. Samples are drawn from two different populations such that there is a matching of the first sample data drawn and a corresponding data value in the second sample data.
Dependent Selection
A population or statistical population
A random variable
Bias
27. (also called statistical variability) is a measure of how diverse some data is. It can be expressed by the variance or the standard deviation.
A probability space
Statistical dispersion
Statistics
nominal - ordinal - interval - and ratio
28. Is the length of the smallest interval which contains all the data.
The Range
Type I errors & Type II errors
Descriptive
That is the median value
29. Cov[X - Y] :
covariance of X and Y
Parameter
Probability density functions
Pairwise independence
30. 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.
Descriptive statistics
Sampling Distribution
methods of least squares
That value is the median value
31. 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
Average and arithmetic mean
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
observational study
32. Have no meaningful rank order among values.
Nominal measurements
Simpson's Paradox
Binary data
Kurtosis
33. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
Trend
That value is the median value
Conditional probability
Sampling Distribution
34. 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.
Step 1 of a statistical experiment
Beta value
Bias
the population variance
35. A data value that falls outside the overall pattern of the graph.
Probability density
Ordinal measurements
Atomic event
Outlier
36. Used to reduce bias - this measure weights the more relevant information higher than less relevant info.
Divide the sum by the number of values.
Statistical adjustment
Coefficient of determination
A statistic
37. Statistical methods can be used for summarizing or describing a collection of data; this is called
A Distribution function
descriptive statistics
An estimate of a parameter
hypothesis
38. Probability of rejecting a true null hypothesis.
Independent Selection
Alpha value (Level of Significance)
the population correlation
Residuals
39. 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
Statistical dispersion
Descriptive
inferential statistics
Variable
40. Descriptive statistics and inferential statistics (a.k.a. - predictive statistics) together comprise
A probability density function
Bias
applied statistics
Simple random sample
41. Of a group of numbers is the center point of all those number values.
Residuals
Independent Selection
The average - or arithmetic mean
Trend
42. (or expectation) of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by its payoff ('value'). Thus - it represents the average amount one 'expects' to win per bet if bets with identical odds are re
Reliable measure
The Expected value
Type I errors
Parameter - or 'statistical parameter'
43. Where the null hypothesis is falsely rejected giving a 'false positive'.
Quantitative variable
Type I errors
Standard error
Binary data
44. Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically - sometimes they are grouped together as
That is the median value
Interval measurements
the population cumulants
categorical variables
45. The proportion of the explained variation by a linear regression model in the total variation.
Coefficient of determination
Probability and statistics
Sampling frame
Mutual independence
46. A scale that represents an ordinal scale such as looks on a scale from 1 to 10.
f(z) - and its cdf by F(z).
The median value
covariance of X and Y
Likert scale
47. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.
Descriptive
A random variable
Marginal probability
the population correlation
48. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively
Parameter - or 'statistical parameter'
Sample space
the population variance
Residuals
49. Statistics involve methods of using information from a sample to draw conclusions regarding the population.
Inferential
A statistic
Statistical adjustment
experimental studies and observational studies.
50. 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.
Probability and statistics
The median value
Sample space
Seasonal effect
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