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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.
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. Probability of rejecting a true null hypothesis.
Alpha value (Level of Significance)
An experimental study
Binary data
The Mean of a random variable
2. Many statistical methods seek to minimize the mean-squared error - and these are called
Beta value
Type 2 Error
methods of least squares
the population correlation
3. Data are gathered and correlations between predictors and response are investigated.
observational study
Independence or Statistical independence
variance of X
inferential statistics
4. A list of individuals from which the sample is actually selected.
A sample
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
The Expected value
Sampling frame
5. 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}.
Joint probability
An event
Step 2 of a statistical experiment
The sample space
6. Statistics involve methods of using information from a sample to draw conclusions regarding the population.
Greek letters
Type 1 Error
Random variables
Inferential
7. 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
Bias
Power of a test
Ratio measurements
Simpson's Paradox
8. 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
Kurtosis
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
A Probability measure
9. Is its expected value. The mean (or sample mean of a data set is just the average value.
Quantitative variable
quantitative variables
The Mean of a random variable
descriptive statistics
10. Is that part of a population which is actually observed.
The variance of a random variable
Type I errors & Type II errors
A sample
Outlier
11. Two variables such that their effects on the response variable cannot be distinguished from each other.
The Covariance between two random variables X and Y - with expected values E(X) =
Quantitative variable
Confounded variables
Law of Large Numbers
12. 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
Conditional distribution
covariance of X and Y
Null hypothesis
A data set
13. Is data that can take only two values - usually represented by 0 and 1.
Binary data
A data point
Residuals
s-algebras
14. 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.
Statistical inference
nominal - ordinal - interval - and ratio
Seasonal effect
Parameter - or 'statistical parameter'
15. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
P-value
The Covariance between two random variables X and Y - with expected values E(X) =
Valid measure
Sample space
16. 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.
Conditional distribution
Standard error
Parameter
inferential statistics
17. 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.
Variability
Coefficient of determination
Bias
The median value
18. A numerical measure that describes an aspect of a sample.
An estimate of a parameter
Statistic
Independence or Statistical independence
Simulation
19. Used to reduce bias - this measure weights the more relevant information higher than less relevant info.
Null hypothesis
Alpha value (Level of Significance)
Outlier
Statistical adjustment
20. 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
An estimate of a parameter
The Range
A Distribution function
Independence or Statistical independence
21. 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
Simulation
Probability density
Type I errors
Conditional probability
22. 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.
Coefficient of determination
Bias
Marginal probability
Type I errors
23. Is the probability of an event - ignoring any information about other events. The marginal probability of A is written P(A). Contrast with conditional probability.
Marginal probability
s-algebras
hypothesis
That value is the median value
24. 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.
methods of least squares
Simple random sample
Correlation coefficient
Bias
25. 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.
Posterior probability
Simple random sample
That value is the median value
The variance of a random variable
26. A group of individuals sharing some common features that might affect the treatment.
Type 1 Error
Marginal distribution
Block
Confounded variables
27. 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
The Range
Simple random sample
Simpson's Paradox
28. Design of experiments - using blocking to reduce the influence of confounding variables - and randomized assignment of treatments to subjects to allow unbiased estimates of treatment effects and experimental error. At this stage - the experimenters a
Type II errors
A probability distribution
Inferential statistics
Step 2 of a statistical experiment
29. A numerical measure that assesses the strength of a linear relationship between two variables.
Seasonal effect
Correlation coefficient
The Range
Independence or Statistical independence
30. Another name for elementary event.
Sample space
Conditional distribution
quantitative variables
Atomic event
31. Is a function that gives the probability of all elements in a given space: see List of probability distributions
Cumulative distribution functions
The sample space
A probability distribution
Type I errors & Type II errors
32. A subjective estimate of probability.
The Range
Credence
expected value of X
Beta value
33. 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'
the population correlation
Bias
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Conditional probability
34. Where the null hypothesis fails to be rejected and an actual difference between populations is missed giving a 'false negative'.
Power of a test
Bias
Type II errors
Statistical inference
35. (also called statistical variability) is a measure of how diverse some data is. It can be expressed by the variance or the standard deviation.
Binomial experiment
Inferential
Lurking variable
Statistical dispersion
36. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
nominal - ordinal - interval - and ratio
The Mean of a random variable
Kurtosis
Marginal distribution
37. Is defined as the expected value of random variable (X -
hypothesis
the population correlation
Atomic event
The Covariance between two random variables X and Y - with expected values E(X) =
38. The probability of correctly detecting a false null hypothesis.
Parameter - or 'statistical parameter'
A random variable
Kurtosis
Power of a test
39. In number theory - scatter plots of data generated by a distribution function may be transformed with familiar tools used in statistics to reveal underlying patterns - which may then lead to
expected value of X
Type II errors
Beta value
hypotheses
40. A data value that falls outside the overall pattern of the graph.
Outlier
Probability density
An event
Marginal distribution
41. The standard deviation of a sampling distribution.
hypotheses
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
The Mean of a random variable
Standard error
42. Summarize the population data by describing what was observed in the sample numerically or graphically. Numerical descriptors include mean and standard deviation for continuous data types (like heights or weights) - while frequency and percentage are
Binomial experiment
Descriptive statistics
Variable
Block
43. 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
A probability space
Law of Parsimony
An experimental study
Probability and statistics
44. 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).
Type I errors
Placebo effect
An event
Marginal distribution
45. (or multivariate random variable) is a vector whose components are random variables on the same probability space.
inferential statistics
The sample space
The standard deviation
A Random vector
46. The collection of all possible outcomes in an experiment.
Sample space
Variable
Cumulative distribution functions
A probability density function
47. A measure that is relevant or appropriate as a representation of that property.
Marginal distribution
Individual
f(z) - and its cdf by F(z).
Valid measure
48. The result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data
A sampling distribution
Posterior probability
Dependent Selection
The average - or arithmetic mean
49. Are simply two different terms for the same thing. Add the given values
expected value of X
An estimate of a parameter
Type II errors
Average and arithmetic mean
50. 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.
inferential statistics
Qualitative variable
Dependent Selection
Likert scale