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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. When there is an even number of values...
An experimental study
Sampling frame
That is the median value
s-algebras
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.
Ratio measurements
A probability distribution
Marginal distribution
Statistical dispersion
3. Have imprecise differences between consecutive values - but have a meaningful order to those values
Probability density
s-algebras
Ordinal measurements
Statistical dispersion
4. 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
Sample space
Kurtosis
hypothesis
the population mean
5. Long-term upward or downward movement over time.
Trend
Random variables
Interval measurements
A probability space
6. Two variables such that their effects on the response variable cannot be distinguished from each other.
Skewness
Dependent Selection
the population mean
Confounded variables
7. Rejecting a true null hypothesis.
Residuals
Confounded variables
Inferential
Type 1 Error
8. (or multivariate random variable) is a vector whose components are random variables on the same probability space.
the population mean
A Random vector
Sampling frame
Individual
9. Is defined as the expected value of random variable (X -
The Covariance between two random variables X and Y - with expected values E(X) =
Skewness
Simpson's Paradox
Posterior probability
10. Consists of a number of independent trials repeated under identical conditions. On each trial - there are two possible outcomes.
f(z) - and its cdf by F(z).
Skewness
Binomial experiment
Alpha value (Level of Significance)
11. S^2
Statistic
the population variance
Estimator
The average - or arithmetic mean
12. In particular - the pdf of the standard normal distribution is denoted by
the sample or population mean
f(z) - and its cdf by F(z).
Statistic
A sample
13. 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.
Seasonal effect
A data point
Type 2 Error
Probability
14. 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.
Estimator
Correlation
A data point
A statistic
15. 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.
inferential statistics
Conditional distribution
Inferential statistics
Nominal measurements
16. Is a parameter that indexes a family of probability distributions.
Independence or Statistical independence
Probability density functions
A Statistical parameter
A sample
17. 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
nominal - ordinal - interval - and ratio
Independence or Statistical independence
Sampling frame
Dependent Selection
18. 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
Type 1 Error
Observational study
A sample
the population mean
19. (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
Law of Parsimony
Probability density
A likelihood function
Beta value
20. Gives the probability of events in a probability space.
the population variance
A Probability measure
Parameter
s-algebras
21. Of a group of numbers is the center point of all those number values.
expected value of X
Law of Parsimony
The average - or arithmetic mean
Bias
22. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.
Bias
Quantitative variable
Inferential statistics
Descriptive
23. Var[X] :
variance of X
Parameter
observational study
Experimental and observational studies
24. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
Null hypothesis
Law of Large Numbers
variance of X
Power of a test
25. (e.g. ? - b) are commonly used to denote unknown parameters (population parameters).
Greek letters
A sampling distribution
Inferential
Conditional probability
26. Are usually written with upper case calligraphic (e.g. F for the set of sets on which we define the probability P)
s-algebras
Bias
That value is the median value
A population or statistical population
27. A list of individuals from which the sample is actually selected.
A Statistical parameter
Bias
Sampling frame
Probability density
28. 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
Residuals
The variance of a random variable
Sampling Distribution
Probability and statistics
29. 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 Expected value
inferential statistics
Parameter - or 'statistical parameter'
Lurking variable
30. The proportion of the explained variation by a linear regression model in the total variation.
Coefficient of determination
Type II errors
A Distribution function
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
31. Are simply two different terms for the same thing. Add the given values
Average and arithmetic mean
The variance of a random variable
Credence
descriptive statistics
32. Data are gathered and correlations between predictors and response are investigated.
The average - or arithmetic mean
nominal - ordinal - interval - and ratio
observational study
A Random vector
33. Is denoted by - pronounced 'x bar'.
Descriptive statistics
the population correlation
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
covariance of X and Y
34. 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
Null hypothesis
Placebo effect
Bias
Valid measure
35. A scale that represents an ordinal scale such as looks on a scale from 1 to 10.
Outlier
Likert scale
Bias
Mutual independence
36. Samples are drawn from two different populations such that there is a matching of the first sample data drawn and a corresponding data value in the second sample data.
Dependent Selection
An event
Conditional probability
Step 2 of a statistical experiment
37. 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).
covariance of X and Y
Joint probability
Independence or Statistical independence
Binary data
38. Working from a null hypothesis two basic forms of error are recognized:
An Elementary event
Mutual independence
Type I errors & Type II errors
Bias
39. Probability of rejecting a true null hypothesis.
hypothesis
Lurking variable
Alpha value (Level of Significance)
Posterior probability
40. A numerical measure that describes an aspect of a population.
Probability
Parameter - or 'statistical parameter'
Parameter
the population mean
41. Many statistical methods seek to minimize the mean-squared error - and these are called
A sample
Correlation
methods of least squares
That value is the median value
42. Where the null hypothesis fails to be rejected and an actual difference between populations is missed giving a 'false negative'.
descriptive statistics
A Distribution function
experimental studies and observational studies.
Type II errors
43. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
Conditional distribution
Sampling Distribution
variance of X
hypotheses
44. A consistent - repeated deviation of the sample statistic from the population parameter in the same direction when many samples are taken.
Prior probability
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Bias
That is the median value
45. Are written in corresponding lower case letters. For example x1 - x2 - ... - xn could be a sample corresponding to the random variable X.
A probability space
Particular realizations of a random variable
Step 2 of a statistical experiment
Joint probability
46. Cov[X - Y] :
hypothesis
covariance of X and Y
Step 1 of a statistical experiment
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
47. 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.
Statistics
Binary data
Statistical inference
Alpha value (Level of Significance)
48. ?
Independence or Statistical independence
Individual
A sample
the population correlation
49. 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.
A data set
Skewness
Binary data
The variance of a random variable
50. 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
Correlation coefficient
Experimental and observational studies
Credence
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