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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. ?r
Null hypothesis
the population cumulants
Bias
Ratio measurements
2. In particular - the pdf of the standard normal distribution is denoted by
nominal - ordinal - interval - and ratio
An Elementary event
the population mean
f(z) - and its cdf by F(z).
3. Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically - sometimes they are grouped together as
Probability density functions
categorical variables
Inferential
nominal - ordinal - interval - and ratio
4. Is a measure of the 'peakedness' of the probability distribution of a real-valued random variable. Higher kurtosis means more of the variance is due to infrequent extreme deviations - as opposed to frequent modestly sized deviations.
A Probability measure
Standard error
Kurtosis
variance of X
5. Are usually written in upper case roman letters: X - Y - etc.
observational study
P-value
Binomial experiment
Random variables
6. 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}.
expected value of X
Block
Power of a test
The sample space
7. Var[X] :
Inferential statistics
Probability density
That is the median value
variance of X
8. Some commonly used symbols for sample statistics
The variance of a random variable
Sampling frame
Lurking variable
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
9. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
Independence or Statistical independence
The Range
Pairwise independence
Parameter
10. 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
Estimator
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
the population cumulants
Independence or Statistical independence
11. 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
The Range
experimental studies and observational studies.
Probability density
inferential statistics
12. Is the most commonly used measure of statistical dispersion. It is the square root of the variance - and is generally written s (sigma).
A likelihood function
Posterior probability
The standard deviation
A probability distribution
13. 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.
Sampling
Conditional probability
experimental studies and observational studies.
Prior probability
14. Of a group of numbers is the center point of all those number values.
The average - or arithmetic mean
A sampling distribution
Interval measurements
Type I errors
15. A numerical measure that describes an aspect of a population.
Simpson's Paradox
Sampling
Parameter
Likert scale
16. Is a sample space over which a probability measure has been defined.
Step 3 of a statistical experiment
Experimental and observational studies
A probability space
Prior probability
17. Is denoted by - pronounced 'x bar'.
Inferential
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Bias
experimental studies and observational studies.
18. 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
Simple random sample
Trend
Treatment
Correlation
19. Is the probability of some event A - assuming event B. Conditional probability is written P(A|B) - and is read 'the probability of A - given B'
Conditional probability
Prior probability
Probability density
Confounded variables
20. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
Posterior probability
Step 2 of a statistical experiment
P-value
Outlier
21. The proportion of the explained variation by a linear regression model in the total variation.
the population mean
Coefficient of determination
Law of Large Numbers
Simple random sample
22. Two variables such that their effects on the response variable cannot be distinguished from each other.
Confounded variables
Independence or Statistical independence
Descriptive statistics
A data set
23. 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
Count data
Inferential statistics
A sampling distribution
hypothesis
24. Is a parameter that indexes a family of probability distributions.
A Statistical parameter
A likelihood function
Law of Parsimony
Joint probability
25. To find the average - or arithmetic mean - of a set of numbers:
Marginal distribution
Step 2 of a statistical experiment
Divide the sum by the number of values.
Probability density
26. Is data arising from counting that can take only non-negative integer values.
Step 2 of a statistical experiment
Parameter - or 'statistical parameter'
nominal - ordinal - interval - and ratio
Count data
27. 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).
variance of X
Independent Selection
Valid measure
Joint probability
28. Is the length of the smallest interval which contains all the data.
Type I errors
The Range
Probability density functions
Joint probability
29. 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.
Ordinal measurements
Independent Selection
A data point
Count data
30. 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
the population mean
Sampling frame
Step 3 of a statistical experiment
Treatment
31. Have meaningful distances between measurements defined - but the zero value is arbitrary (as in the case with longitude and temperature measurements in Celsius or Fahrenheit)
Probability density
Interval measurements
A sample
Law of Large Numbers
32. Long-term upward or downward movement over time.
A probability distribution
Trend
hypothesis
Independent Selection
33. The probability of correctly detecting a false null hypothesis.
Step 1 of a statistical experiment
Power of a test
Confounded variables
A Statistical parameter
34. Describes a characteristic of an individual to be measured or observed.
Simulation
nominal - ordinal - interval - and ratio
Variable
The median value
35. ?
Sample space
Experimental and observational studies
categorical variables
the population correlation
36. A measurement such that the random error is small
Particular realizations of a random variable
Nominal measurements
Reliable measure
Greek letters
37. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.
Greek letters
Descriptive
Dependent Selection
Binomial experiment
38. A subjective estimate of probability.
The average - or arithmetic mean
The variance of a random variable
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Credence
39. Is that part of a population which is actually observed.
nominal - ordinal - interval - and ratio
Joint distribution
the sample or population mean
A sample
40. 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
Marginal distribution
An event
Inferential
41. A scale that represents an ordinal scale such as looks on a scale from 1 to 10.
A probability space
Likert scale
Divide the sum by the number of values.
Greek letters
42. 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
An event
Binomial experiment
Null hypothesis
Statistic
43. 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
A probability space
Simpson's Paradox
Descriptive
44. Working from a null hypothesis two basic forms of error are recognized:
Step 1 of a statistical experiment
An estimate of a parameter
Type I errors & Type II errors
Trend
45. A group of individuals sharing some common features that might affect the treatment.
Block
Law of Parsimony
Quantitative variable
A data set
46. 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
Statistic
expected value of X
Statistical adjustment
Probability
47. (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
Inferential statistics
A likelihood function
the sample or population mean
Parameter - or 'statistical parameter'
48. Gives the probability of events in a probability space.
A Probability measure
Descriptive statistics
Independent Selection
Probability density
49. The result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data
Mutual independence
The Expected value
Posterior probability
An estimate of a parameter
50. A numerical measure that assesses the strength of a linear relationship between two variables.
Statistical adjustment
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Correlation coefficient
Null hypothesis
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