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Test your basic knowledge |
CLEP General Mathematics: Probability And Statistics
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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 sample statistics
Experimental and observational studies
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Trend
A Probability measure
2. (also called statistical variability) is a measure of how diverse some data is. It can be expressed by the variance or the standard deviation.
Skewness
Statistical dispersion
Sampling
Variable
3. Another name for elementary event.
Atomic event
Type I errors & Type II errors
Correlation coefficient
Valid measure
4. 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.
Confounded variables
Seasonal effect
The sample space
Pairwise independence
5. The standard deviation of a sampling distribution.
Statistical adjustment
The Mean of a random variable
Likert scale
Standard error
6. 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
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Beta value
Ratio measurements
A data set
7. The probability of correctly detecting a false null hypothesis.
Binomial experiment
Power of a test
quantitative variables
Simple random sample
8. Failing to reject a false null hypothesis.
Simple random sample
Greek letters
Marginal distribution
Type 2 Error
9. A numerical measure that describes an aspect of a sample.
The median value
Statistic
Probability density
Sample space
10. E[X] :
Statistic
Average and arithmetic mean
Binomial experiment
expected value of X
11. 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.
That value is the median value
Confounded variables
descriptive statistics
Sampling Distribution
12. (or multivariate random variable) is a vector whose components are random variables on the same probability space.
Step 1 of a statistical experiment
Inferential statistics
Ratio measurements
A Random vector
13. 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
Type II errors
Correlation
Probability density
A Distribution function
14. Data are gathered and correlations between predictors and response are investigated.
observational study
Inferential
Simple random sample
f(z) - and its cdf by F(z).
15. Is data that can take only two values - usually represented by 0 and 1.
Credence
The standard deviation
Simpson's Paradox
Binary data
16. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
Interval measurements
Law of Parsimony
Skewness
Pairwise independence
17. 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).
Variability
Step 2 of a statistical experiment
Joint distribution
An event
18. Is the probability of two events occurring together. The joint probability of A and B is written P(A and B) or P(A - B).
Outlier
Likert scale
A Random vector
Joint probability
19. Probability of accepting a false null hypothesis.
Beta value
Step 2 of a statistical experiment
Divide the sum by the number of values.
Prior probability
20. Describes the spread in the values of the sample statistic when many samples are taken.
Simple random sample
Type II errors
Variability
Alpha value (Level of Significance)
21. Probability of rejecting a true null hypothesis.
methods of least squares
Alpha value (Level of Significance)
Experimental and observational studies
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
22. 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.
Reliable measure
Experimental and observational studies
Marginal distribution
The sample space
23. 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.
Nominal measurements
Mutual independence
the population variance
Conditional distribution
24. ?
Law of Parsimony
the population correlation
The variance of a random variable
the population variance
25. 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
f(z) - and its cdf by F(z).
Type I errors & Type II errors
A likelihood function
26. 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
A Statistical parameter
Pairwise independence
Divide the sum by the number of values.
experimental studies and observational studies.
27. Statistics involve methods of using information from a sample to draw conclusions regarding the population.
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
the sample or population mean
Inferential
Ratio measurements
28. Is the probability distribution - under repeated sampling of the population - of a given statistic.
Valid measure
f(z) - and its cdf by F(z).
A sampling distribution
Experimental and observational studies
29. Are usually written with upper case calligraphic (e.g. F for the set of sets on which we define the probability P)
A sampling distribution
Posterior probability
s-algebras
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
30. Given two random variables X and Y - the joint distribution of X and Y is the probability distribution of X and Y together.
Lurking variable
A statistic
Parameter
Joint distribution
31. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
Trend
A sampling distribution
Sampling frame
Prior probability
32. A variable has a value or numerical measurement for which operations such as addition or averaging make sense.
the population variance
Statistical adjustment
Quantitative variable
The Covariance between two random variables X and Y - with expected values E(X) =
33. (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.
Bias
Type II errors
A sampling distribution
An Elementary event
34. Is the function that gives the probability distribution of a random variable. It cannot be negative - and its integral on the probability space is equal to 1.
Type II errors
Quantitative variable
A Distribution function
Probability and statistics
35. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
Coefficient of determination
A probability distribution
Sampling Distribution
Marginal probability
36. Gives the probability distribution for a continuous random variable.
Average and arithmetic mean
Standard error
A probability density function
Type II errors
37. 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.
Nominal measurements
Simple random sample
Statistic
Block
38. Consists of a number of independent trials repeated under identical conditions. On each trial - there are two possible outcomes.
Marginal probability
An estimate of a parameter
Binomial experiment
s-algebras
39. 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
Type I errors
Bias
Dependent Selection
40. A list of individuals from which the sample is actually selected.
Conditional distribution
Null hypothesis
Sampling frame
A probability density function
41. 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
A population or statistical population
Random variables
the population correlation
42. Is defined as the expected value of random variable (X -
Block
The Covariance between two random variables X and Y - with expected values E(X) =
The median value
s-algebras
43. Is the length of the smallest interval which contains all the data.
A population or statistical population
observational study
Independent Selection
The Range
44. Can be - for example - the possible outcomes of a dice roll (but it is not assigned a value). The distribution function of a random variable gives the probability of different results. We can also derive the mean and variance of a random variable.
Reliable measure
Type II errors
Ordinal measurements
A random variable
45. 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.
hypothesis
A Random vector
Statistics
A population or statistical population
46. 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.
Inferential statistics
Independent Selection
A data point
inferential statistics
47. 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
Probability density functions
Marginal probability
the population cumulants
48. Is denoted by - pronounced 'x bar'.
Sampling Distribution
Binomial experiment
Residuals
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
49. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
Alpha value (Level of Significance)
The median value
A Statistical parameter
Law of Large Numbers
50. Is a process of selecting observations to obtain knowledge about a population. There are many methods to choose on which sample to do the observations.
Binomial experiment
A probability density function
Posterior probability
Sampling