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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. (pdfs) and probability mass functions are denoted by lower case letters - e.g. f(x).
Reliable measure
Probability density functions
Beta value
An estimate of a parameter
2. Is a parameter that indexes a family of probability distributions.
A Statistical parameter
The standard deviation
Seasonal effect
A random variable
3. Is the most commonly used measure of statistical dispersion. It is the square root of the variance - and is generally written s (sigma).
Simple random sample
expected value of X
The standard deviation
A likelihood function
4. Is a sample space over which a probability measure has been defined.
A probability space
An event
the population mean
the sample or population mean
5. A measurement such that the random error is small
That is the median value
Statistic
P-value
Reliable measure
6. 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
Count data
expected value of X
Parameter
Skewness
7. 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
An event
Mutual independence
Qualitative variable
Likert scale
8. Some commonly used symbols for population parameters
A probability density function
hypotheses
Variability
the population mean
9. 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.
An experimental study
A population or statistical population
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Kurtosis
10. Descriptive statistics and inferential statistics (a.k.a. - predictive statistics) together comprise
Coefficient of determination
A Statistical parameter
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
applied statistics
11. Working from a null hypothesis two basic forms of error are recognized:
Type I errors & Type II errors
Lurking variable
Treatment
Coefficient of determination
12. Is the probability distribution - under repeated sampling of the population - of a given statistic.
A sampling distribution
A sample
A probability space
The Expected value
13. The collection of all possible outcomes in an experiment.
Sample space
A Distribution function
Prior probability
Correlation coefficient
14. (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
The Expected value
The Covariance between two random variables X and Y - with expected values E(X) =
Statistic
Probability density
15. 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
Posterior probability
Ratio measurements
hypotheses
A likelihood function
16. Cov[X - Y] :
Simpson's Paradox
Skewness
Type 2 Error
covariance of X and Y
17. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.
Credence
Nominal measurements
An estimate of a parameter
Variability
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
Inferential
That is the median value
A population or statistical population
Correlation
19. Failing to reject a false null hypothesis.
Ratio measurements
An experimental study
Type 2 Error
observational study
20. 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
A random variable
Qualitative variable
Inferential statistics
Step 1 of a statistical experiment
21. Is the length of the smallest interval which contains all the data.
Estimator
Inferential
Law of Parsimony
The Range
22. 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.
The variance of a random variable
expected value of X
hypotheses
Experimental and observational studies
23. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.
Probability
The median value
Binary data
Descriptive
24. 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
Count data
Law of Large Numbers
Individual
25. Data are gathered and correlations between predictors and response are investigated.
The Range
Simpson's Paradox
observational study
That value is the median value
26. The proportion of the explained variation by a linear regression model in the total variation.
A Statistical parameter
An Elementary event
Coefficient of determination
Sampling frame
27. Is denoted by - pronounced 'x bar'.
Residuals
Type II errors
The median value
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
28. Have no meaningful rank order among values.
Independence or Statistical independence
The Expected value
Nominal measurements
Trend
29. A group of individuals sharing some common features that might affect the treatment.
Probability density functions
Inferential statistics
Type II errors
Block
30. (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
Independence or Statistical independence
A likelihood function
Likert scale
Variable
31. 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
A sample
Type II errors
Step 1 of a statistical experiment
Independent Selection
32. 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
A statistic
Lurking variable
Observational study
A probability space
33. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Beta value
Residuals
Step 1 of a statistical experiment
34. Of a group of numbers is the center point of all those number values.
A Probability measure
The average - or arithmetic mean
nominal - ordinal - interval - and ratio
A likelihood function
35. 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.
Block
Simple random sample
quantitative variables
A random variable
36. Are two related but separate academic disciplines. Statistical analysis often uses probability distributions - and the two topics are often studied together. However - probability theory contains much that is of mostly of mathematical interest and no
nominal - ordinal - interval - and ratio
Statistical adjustment
Probability and statistics
inferential statistics
37. A scale that represents an ordinal scale such as looks on a scale from 1 to 10.
Likert scale
nominal - ordinal - interval - and ratio
quantitative variables
Estimator
38. 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.
Beta value
Reliable measure
Probability and statistics
That value is the median value
39. E[X] :
Sampling Distribution
expected value of X
descriptive statistics
That is the median value
40. Long-term upward or downward movement over time.
Credence
The Mean of a random variable
Bias
Trend
41. A subjective estimate of probability.
That is the median value
Credence
expected value of X
Probability and statistics
42. To prove the guiding theory further - these predictions are tested as well - as part of the scientific method. If the inference holds true - then the descriptive statistics of the new data increase the soundness of that
Outlier
Step 1 of a statistical experiment
hypothesis
Variability
43. Is its expected value. The mean (or sample mean of a data set is just the average value.
descriptive statistics
The sample space
A Random vector
The Mean of a random variable
44. 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.
Atomic event
Descriptive
Simple random sample
A data point
45. A data value that falls outside the overall pattern of the graph.
Statistics
methods of least squares
Law of Parsimony
Outlier
46. When you have two or more competing models - choose the simpler of the two models.
Variable
Law of Parsimony
Probability
That is the median value
47. 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).
Joint probability
Nominal measurements
The variance of a random variable
Treatment
48. Are written in corresponding lower case letters. For example x1 - x2 - ... - xn could be a sample corresponding to the random variable X.
The standard deviation
Sampling frame
Variable
Particular realizations of a random variable
49. 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}.
Interval measurements
Binomial experiment
Parameter - or 'statistical parameter'
The sample space
50. A list of individuals from which the sample is actually selected.
expected value of X
Sampling frame
Credence
Estimator
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