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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. 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
the population variance
The Covariance between two random variables X and Y - with expected values E(X) =
Probability density
A sampling distribution
2. 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
Variable
the population correlation
A Random vector
Step 1 of a statistical experiment
3. Is the length of the smallest interval which contains all the data.
The Range
Correlation
Variable
Mutual independence
4. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
Simple random sample
Treatment
Block
Law of Large Numbers
5. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
Parameter - or 'statistical parameter'
the population cumulants
Pairwise independence
Marginal distribution
6. E[X] :
Power of a test
Marginal probability
An estimate of a parameter
expected value of X
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
Sampling Distribution
Statistical inference
Standard error
Inferential statistics
8. Are usually written in upper case roman letters: X - Y - etc.
Count data
Simpson's Paradox
Random variables
Joint probability
9. Failing to reject a false null hypothesis.
Credence
Type 2 Error
Bias
hypotheses
10. (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.
Marginal distribution
An Elementary event
A Random vector
A data point
11. 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
Sampling frame
Random variables
The Mean of a random variable
Null hypothesis
12. A consistent - repeated deviation of the sample statistic from the population parameter in the same direction when many samples are taken.
Bias
Reliable measure
The standard deviation
Parameter - or 'statistical parameter'
13. 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
Joint probability
Skewness
Joint distribution
Probability
14. Are usually written with upper case calligraphic (e.g. F for the set of sets on which we define the probability P)
Probability density
A data point
hypothesis
s-algebras
15. In particular - the pdf of the standard normal distribution is denoted by
Placebo effect
Simulation
f(z) - and its cdf by F(z).
Ratio measurements
16. A numerical measure that describes an aspect of a population.
That value is the median value
Parameter
experimental studies and observational studies.
Qualitative variable
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.
A Probability measure
the population variance
Lurking variable
A Random vector
18. Of a group of numbers is the center point of all those number values.
A probability density function
A sample
The average - or arithmetic mean
A data set
19. (cdfs) are denoted by upper case letters - e.g. F(x).
Greek letters
Type I errors & Type II errors
Cumulative distribution functions
The average - or arithmetic mean
20. Is a measure of its statistical dispersion - indicating how far from the expected value its values typically are. The variance of random variable X is typically designated as - - or simply s2.
Cumulative distribution functions
The variance of a random variable
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Block
21. Describes a characteristic of an individual to be measured or observed.
Variable
methods of least squares
Independence or Statistical independence
A likelihood function
22. Working from a null hypothesis two basic forms of error are recognized:
Type I errors & Type II errors
Atomic event
An experimental study
Type II errors
23. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
Cumulative distribution functions
Prior probability
The median value
Simulation
24. Probability of rejecting a true null hypothesis.
Variability
Alpha value (Level of Significance)
Statistics
A Distribution function
25. A numerical measure that describes an aspect of a sample.
Statistic
Independent Selection
Dependent Selection
An estimate of a parameter
26. 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.
That value is the median value
A population or statistical population
The Expected value
Descriptive statistics
27. A group of individuals sharing some common features that might affect the treatment.
Block
Reliable measure
Sample space
Likert scale
28. 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.
Binomial experiment
Conditional probability
Statistical inference
categorical variables
29. Have no meaningful rank order among values.
Likert scale
A sample
Nominal measurements
Sampling Distribution
30. Is data arising from counting that can take only non-negative integer values.
Correlation
Count data
Quantitative variable
The variance of a random variable
31. 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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32. To find the average - or arithmetic mean - of a set of numbers:
A data set
Divide the sum by the number of values.
Null hypothesis
Statistical dispersion
33. Is a parameter that indexes a family of probability distributions.
The Covariance between two random variables X and Y - with expected values E(X) =
Null hypothesis
Marginal probability
A Statistical parameter
34. 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.
Independence or Statistical independence
the population variance
Outlier
The median value
35. 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.
Experimental and observational studies
hypothesis
Correlation
Average and arithmetic mean
36. Two variables such that their effects on the response variable cannot be distinguished from each other.
the population variance
Confounded variables
Credence
Independence or Statistical independence
37. When there is an even number of values...
Placebo effect
Random variables
The standard deviation
That is the median value
38. 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}.
A data point
The sample space
Posterior probability
Statistical adjustment
39. 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
Binomial experiment
experimental studies and observational studies.
Descriptive
Correlation coefficient
40. Cov[X - Y] :
Likert scale
An Elementary event
covariance of X and Y
Type II errors
41. Used to reduce bias - this measure weights the more relevant information higher than less relevant info.
Statistical adjustment
A random variable
Experimental and observational studies
Alpha value (Level of Significance)
42. Are simply two different terms for the same thing. Add the given values
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
applied statistics
Average and arithmetic mean
Type II errors
43. 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
Independent Selection
Conditional distribution
f(z) - and its cdf by F(z).
44. The proportion of the explained variation by a linear regression model in the total variation.
Descriptive statistics
The Range
Probability
Coefficient of determination
45. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively
The Mean of a random variable
the population cumulants
Inferential
Residuals
46. 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
Observational study
Power of a test
A sample
Reliable measure
47. (also called statistical variability) is a measure of how diverse some data is. It can be expressed by the variance or the standard deviation.
That value is the median value
variance of X
Kurtosis
Statistical dispersion
48. 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
hypothesis
Independence or Statistical independence
A population or statistical population
A Probability measure
49. Gives the probability distribution for a continuous random variable.
A probability density function
Alpha value (Level of Significance)
Credence
Marginal distribution
50. A numerical facsimilie or representation of a real-world phenomenon.
Simulation
The sample space
Statistical inference
Statistical dispersion