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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. 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.
An estimate of a parameter
Independence or Statistical independence
Sampling
Pairwise independence
2. 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
Binomial experiment
Valid measure
Interval measurements
Inferential statistics
3. Describes the spread in the values of the sample statistic when many samples are taken.
Variability
The sample space
A statistic
Step 1 of a statistical experiment
4. Is data arising from counting that can take only non-negative integer values.
Count data
Parameter
Statistical inference
A likelihood function
5. Given two random variables X and Y - the joint distribution of X and Y is the probability distribution of X and Y together.
A Random vector
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Statistical adjustment
Joint distribution
6. Can be a population parameter - a distribution parameter - an unobserved parameter (with different shades of meaning). In statistics - this is often a quantity to be estimated.
7. The standard deviation of a sampling distribution.
Reliable measure
Individual
The average - or arithmetic mean
Standard error
8. Var[X] :
inferential statistics
variance of X
A statistic
Divide the sum by the number of values.
9. 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
The median value
the population mean
inferential statistics
Descriptive statistics
10. The proportion of the explained variation by a linear regression model in the total variation.
Coefficient of determination
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
P-value
Random variables
11. 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
Step 2 of a statistical experiment
hypothesis
descriptive statistics
nominal - ordinal - interval - and ratio
12. 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
Skewness
Trend
Step 1 of a statistical experiment
The Covariance between two random variables X and Y - with expected values E(X) =
13. (also called statistical variability) is a measure of how diverse some data is. It can be expressed by the variance or the standard deviation.
Statistical dispersion
Pairwise independence
Alpha value (Level of Significance)
A data set
14. 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.
Posterior probability
Joint probability
Dependent Selection
Ordinal measurements
15. The probability of correctly detecting a false null hypothesis.
Simulation
A statistic
Power of a test
s-algebras
16. A variable describes an individual by placing the individual into a category or a group.
Placebo effect
Qualitative variable
The average - or arithmetic mean
the population mean
17. A subjective estimate of probability.
Correlation coefficient
That value is the median value
Credence
Mutual independence
18. Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically - sometimes they are grouped together as
Probability and statistics
Trend
categorical variables
A sampling distribution
19. 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.
Treatment
Variability
Count data
The median value
20. A numerical measure that describes an aspect of a sample.
Descriptive
hypothesis
Statistic
Coefficient of determination
21. Gives the probability distribution for a continuous random variable.
Mutual independence
A probability density function
P-value
Simple random sample
22. Probability of accepting a false null hypothesis.
Step 1 of a statistical experiment
A sample
Beta value
The sample space
23. Where the null hypothesis fails to be rejected and an actual difference between populations is missed giving a 'false negative'.
Count data
Type II errors
Individual
Interval measurements
24. Statistics involve methods of using information from a sample to draw conclusions regarding the population.
An estimate of a parameter
descriptive statistics
Inferential
That value is the median value
25. Some commonly used symbols for population parameters
Residuals
the population mean
Type I errors
inferential statistics
26. (or atomic event) is an event with only one element. For example - when pulling a card out of a deck - 'getting the jack of spades' is an elementary event - while 'getting a king or an ace' is not.
That is the median value
Independent Selection
Statistics
An Elementary event
27. 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.
the population cumulants
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
An Elementary event
Marginal probability
28. 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
Simulation
experimental studies and observational studies.
Sample space
29. 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
Observational study
Binary data
Ratio measurements
Simulation
30. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.
Type I errors
Sampling
An estimate of a parameter
Inferential statistics
31. 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
hypotheses
A Statistical parameter
A Random vector
The average - or arithmetic mean
32. Is denoted by - pronounced 'x bar'.
Law of Large Numbers
Quantitative variable
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Qualitative variable
33. Consists of a number of independent trials repeated under identical conditions. On each trial - there are two possible outcomes.
Probability
Simpson's Paradox
hypotheses
Binomial experiment
34. There are two major types of causal statistical studies: In both types of studies - the effect of differences of an independent variable (or variables) on the behavior of the dependent variable are observed. The difference between the two types lies
Ordinal measurements
Type 2 Error
experimental studies and observational studies.
Probability density functions
35. Have no meaningful rank order among values.
Qualitative variable
Interval measurements
Descriptive
Nominal measurements
36. Statistical methods can be used for summarizing or describing a collection of data; this is called
Type I errors
descriptive statistics
Kurtosis
Marginal distribution
37. The result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data
Conditional probability
A probability density function
Posterior probability
A Statistical parameter
38. 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
inferential statistics
Divide the sum by the number of values.
Descriptive
Ordinal measurements
39. A numerical measure that describes an aspect of a population.
Parameter
A Statistical parameter
Statistical dispersion
Statistical inference
40. Samples are drawn from two different populations such that the sample data drawn from one population is completely unrelated to the selection of sample data from the other population.
Mutual independence
Bias
Independent Selection
Correlation coefficient
41. (pdfs) and probability mass functions are denoted by lower case letters - e.g. f(x).
Probability density functions
Independence or Statistical independence
Power of a test
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
42. (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
Placebo effect
Correlation
A likelihood function
Likert scale
43. A variable that has an important effect on the response variable and the relationship among the variables in a study but is not one of the explanatory variables studied either because it is unknown or not measured.
That is the median value
Lurking variable
Standard error
Valid measure
44. 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
Statistic
Bias
the sample or population mean
45. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
Power of a test
Statistic
Statistical dispersion
Law of Large Numbers
46. 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.
Marginal distribution
Type I errors
Power of a test
A population or statistical population
47. Some commonly used symbols for sample statistics
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
hypotheses
Prior probability
The Expected value
48. (or multivariate random variable) is a vector whose components are random variables on the same probability space.
Count data
Standard error
A Random vector
A population or statistical population
49. 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 average - or arithmetic mean
Step 3 of a statistical experiment
The median value
inferential statistics
50. Data are gathered and correlations between predictors and response are investigated.
A Statistical parameter
Inferential statistics
The median value
observational study