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Test your basic knowledge |
CLEP General Mathematics: Probability And Statistics
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Study First
Subjects
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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. Some commonly used symbols for population parameters
The Mean of a random variable
the population mean
P-value
The Covariance between two random variables X and Y - with expected values E(X) =
2. 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
A data point
A probability density function
Block
Probability density
3. 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.
observational study
The median value
descriptive statistics
Probability and statistics
4. 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.
Simple random sample
A sampling distribution
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
That is the median value
5. 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 Random vector
the population variance
Correlation
hypothesis
6. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
Bias
The variance of a random variable
nominal - ordinal - interval - and ratio
Cumulative distribution functions
7. 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
A sampling distribution
Pairwise independence
Divide the sum by the number of values.
8. 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.
the population variance
Estimator
Independent Selection
Parameter
9. 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
Placebo effect
That value is the median value
Marginal probability
Inferential statistics
10. A measurement such that the random error is small
Reliable measure
Binomial experiment
A likelihood function
Posterior probability
11. 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.
Variable
Random variables
Statistics
Conditional distribution
12. Is its expected value. The mean (or sample mean of a data set is just the average value.
the population mean
The Mean of a random variable
A population or statistical population
Marginal distribution
13. (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
A likelihood function
Joint distribution
Binomial experiment
Bias
14. Describes a characteristic of an individual to be measured or observed.
Descriptive
Joint probability
The average - or arithmetic mean
Variable
15. To find the average - or arithmetic mean - of a set of numbers:
An Elementary event
A likelihood function
Credence
Divide the sum by the number of values.
16. A variable has a value or numerical measurement for which operations such as addition or averaging make sense.
Quantitative variable
descriptive statistics
Block
A data set
17. Is defined as the expected value of random variable (X -
applied statistics
Sampling
The Covariance between two random variables X and Y - with expected values E(X) =
Probability density functions
18. (or multivariate random variable) is a vector whose components are random variables on the same probability space.
descriptive statistics
A Random vector
Statistical adjustment
Likert scale
19. When you have two or more competing models - choose the simpler of the two models.
Statistic
Sampling
Law of Parsimony
Treatment
20. 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 Distribution function
Ordinal measurements
Atomic event
The sample space
21. Cov[X - Y] :
nominal - ordinal - interval - and ratio
covariance of X and Y
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Inferential statistics
22. Given two random variables X and Y - the joint distribution of X and Y is the probability distribution of X and Y together.
Statistical inference
Joint distribution
Type I errors
Correlation coefficient
23. In particular - the pdf of the standard normal distribution is denoted by
inferential statistics
A random variable
f(z) - and its cdf by F(z).
Atomic event
24. Error also refers to the extent to which individual observations in a sample differ from a central value - such as
the sample or population mean
The Range
That value is the median value
experimental studies and observational studies.
25. Some commonly used symbols for sample statistics
An event
Correlation
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
An experimental study
26. 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.
nominal - ordinal - interval - and ratio
Count data
Marginal distribution
Beta value
27. A numerical measure that assesses the strength of a linear relationship between two variables.
Descriptive statistics
Correlation coefficient
Reliable measure
the population cumulants
28. Have no meaningful rank order among values.
Sampling
Step 1 of a statistical experiment
Simpson's Paradox
Nominal measurements
29. Are simply two different terms for the same thing. Add the given values
Qualitative variable
applied statistics
Average and arithmetic mean
Dependent Selection
30. (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.
The average - or arithmetic mean
An Elementary event
Observational study
Standard error
31. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.
Descriptive
Pairwise independence
the sample or population mean
the population variance
32. Are usually written with upper case calligraphic (e.g. F for the set of sets on which we define the probability P)
s-algebras
Simpson's Paradox
Bias
Ordinal measurements
33. A numerical facsimilie or representation of a real-world phenomenon.
Sampling
Simulation
A sampling distribution
Step 3 of a statistical experiment
34. 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.
Kurtosis
Individual
Observational study
Seasonal effect
35. ?r
A likelihood function
s-algebras
f(z) - and its cdf by F(z).
the population cumulants
36. A variable describes an individual by placing the individual into a category or a group.
Average and arithmetic mean
Posterior probability
Qualitative variable
That value is the median value
37. Is the result of applying a statistical algorithm to a data set. It can also be described as an observable random variable.
Marginal distribution
Beta value
A statistic
categorical variables
38. Probability of rejecting a true null hypothesis.
Step 1 of a statistical experiment
Alpha value (Level of Significance)
Probability and statistics
the population variance
39. The objects described by a set of data: person (animal) - place - and - thing. (SUBJECTS)
Credence
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Kurtosis
Individual
40. Is a typed measurement - it can be a boolean value - a real number - a vector (in which case it's also called a data vector) - etc.
A data point
Type 1 Error
Skewness
covariance of X and Y
41. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
Placebo effect
Descriptive
Pairwise independence
the population cumulants
42. Where the null hypothesis fails to be rejected and an actual difference between populations is missed giving a 'false negative'.
Treatment
Kurtosis
Type II errors
An event
43. 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.
Power of a test
Experimental and observational studies
The standard deviation
A probability density function
44. 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
Step 1 of a statistical experiment
experimental studies and observational studies.
Variable
Coefficient of determination
45. A group of individuals sharing some common features that might affect the treatment.
Mutual independence
descriptive statistics
Credence
Block
46. Ratio and interval measurements which can be either discrete or continuous - due to their numerical nature are grouped together as
Correlation
quantitative variables
That is the median value
Statistical adjustment
47. A numerical measure that describes an aspect of a sample.
experimental studies and observational studies.
Lurking variable
Binomial experiment
Statistic
48. The standard deviation of a sampling distribution.
the population cumulants
Standard error
A sampling distribution
Statistical adjustment
49. Is a parameter that indexes a family of probability distributions.
A Random vector
Conditional distribution
A Statistical parameter
Step 3 of a statistical experiment
50. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
methods of least squares
Sampling Distribution
quantitative variables
Descriptive statistics