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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. (also called statistical variability) is a measure of how diverse some data is. It can be expressed by the variance or the standard deviation.
hypotheses
Statistical dispersion
Marginal distribution
the population mean
2. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.
Reliable measure
Descriptive
Marginal probability
Standard error
3. 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
Type II errors
Joint probability
Inferential statistics
4. Are usually written in upper case roman letters: X - Y - etc.
A Random vector
Reliable measure
Credence
Random variables
5. Where the null hypothesis is falsely rejected giving a 'false positive'.
hypothesis
Type I errors
That is the median value
Type 1 Error
6.
The sample space
the population mean
Placebo effect
Likert scale
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
Sampling
The variance of a random variable
A sample
Ratio measurements
8. Involves taking measurements of the system under study - manipulating the system - and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements.
An experimental study
Probability
Individual
Interval measurements
9. 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
Conditional distribution
the population variance
Cumulative distribution functions
Step 1 of a statistical experiment
10. 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
Average and arithmetic mean
Null hypothesis
experimental studies and observational studies.
Prior probability
11. (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
A likelihood function
Simpson's Paradox
Step 2 of a statistical experiment
Residuals
12. A group of individuals sharing some common features that might affect the treatment.
Step 3 of a statistical experiment
Variable
Block
A Probability measure
13. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
Pairwise independence
An estimate of a parameter
Atomic event
A likelihood function
14. Some commonly used symbols for population parameters
Statistics
Ordinal measurements
the population mean
Type 1 Error
15. 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
Sampling Distribution
Likert scale
Probability
observational study
16. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
applied statistics
nominal - ordinal - interval - and ratio
the population variance
A population or statistical population
17. A data value that falls outside the overall pattern of the graph.
Independent Selection
Outlier
The median value
The Covariance between two random variables X and Y - with expected values E(X) =
18. In particular - the pdf of the standard normal distribution is denoted by
quantitative variables
Alpha value (Level of Significance)
f(z) - and its cdf by F(z).
covariance of X and Y
19. (e.g. ? - b) are commonly used to denote unknown parameters (population parameters).
Greek letters
Coefficient of determination
Placebo effect
Mutual independence
20. A numerical facsimilie or representation of a real-world phenomenon.
the population cumulants
the population correlation
Simulation
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
21. Are written in corresponding lower case letters. For example x1 - x2 - ... - xn could be a sample corresponding to the random variable X.
A likelihood function
the population variance
Inferential statistics
Particular realizations of a random variable
22. A subjective estimate of probability.
Probability density
An event
Credence
Qualitative variable
23. Ratio and interval measurements which can be either discrete or continuous - due to their numerical nature are grouped together as
Inferential statistics
quantitative variables
An event
Valid measure
24. The collection of all possible outcomes in an experiment.
Sample space
Valid measure
quantitative variables
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
25. Is data that can take only two values - usually represented by 0 and 1.
Binary data
Block
Type II errors
Step 2 of a statistical experiment
26. Of a group of numbers is the center point of all those number values.
The average - or arithmetic mean
Simpson's Paradox
Probability density functions
Null hypothesis
27. Is a sample space over which a probability measure has been defined.
the population cumulants
A probability space
descriptive statistics
That value is the median value
28. Descriptive statistics and inferential statistics (a.k.a. - predictive statistics) together comprise
Probability and statistics
applied statistics
The variance of a random variable
Correlation coefficient
29. The proportion of the explained variation by a linear regression model in the total variation.
Marginal distribution
Step 1 of a statistical experiment
The variance of a random variable
Coefficient of determination
30. Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically - sometimes they are grouped together as
An estimate of a parameter
Skewness
categorical variables
Confounded variables
31. Is the result of applying a statistical algorithm to a data set. It can also be described as an observable random variable.
inferential statistics
A statistic
the population cumulants
observational study
32. Given two jointly distributed random variables X and Y - the marginal distribution of X is simply the probability distribution of X ignoring information about Y.
The median value
Quantitative variable
Placebo effect
Marginal distribution
33. 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.
A random variable
Random variables
descriptive statistics
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
34. Many statistical methods seek to minimize the mean-squared error - and these are called
Null hypothesis
An experimental study
methods of least squares
Marginal probability
35. 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).
A likelihood function
Probability density
Joint probability
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
36. Gives the probability of events in a probability space.
Divide the sum by the number of values.
A Probability measure
the population mean
Variability
37. (pdfs) and probability mass functions are denoted by lower case letters - e.g. f(x).
Statistic
Probability density functions
Outlier
Sampling Distribution
38. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
A data point
P-value
methods of least squares
observational study
39. 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
Coefficient of determination
Marginal distribution
Beta value
inferential statistics
40. Data are gathered and correlations between predictors and response are investigated.
A population or statistical population
Descriptive
A Distribution function
observational study
41. Given two random variables X and Y - the joint distribution of X and Y is the probability distribution of X and Y together.
Joint distribution
Probability and statistics
Probability density functions
hypotheses
42. Failing to reject a false null hypothesis.
Descriptive statistics
Type 2 Error
An experimental study
Observational study
43. Statistical methods can be used for summarizing or describing a collection of data; this is called
Step 2 of a statistical experiment
A sample
descriptive statistics
Posterior probability
44. A variable describes an individual by placing the individual into a category or a group.
Qualitative variable
A Distribution function
An experimental study
A probability space
45. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
Law of Large Numbers
P-value
Observational study
nominal - ordinal - interval - and ratio
46. 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'
Marginal probability
A probability distribution
Conditional probability
Simulation
47. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
Prior probability
Marginal distribution
Sampling frame
s-algebras
48. A measurement such that the random error is small
A Distribution function
Statistic
Outlier
Reliable measure
49. 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
Step 2 of a statistical experiment
An event
Mutual independence
Inferential statistics
50. Have no meaningful rank order among values.
A data set
A probability density function
An event
Nominal measurements