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Test your basic knowledge |
CLEP General Mathematics: Probability And Statistics
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clep
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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. The collection of all possible outcomes in an experiment.
Simpson's Paradox
Sample space
s-algebras
f(z) - and its cdf by F(z).
2. Is a function that gives the probability of all elements in a given space: see List of probability distributions
A probability distribution
An estimate of a parameter
The variance of a random variable
Mutual independence
3. Is a sample and the associated data points.
A data set
covariance of X and Y
Correlation coefficient
Prior probability
4. Is a measure of the 'peakedness' of the probability distribution of a real-valued random variable. Higher kurtosis means more of the variance is due to infrequent extreme deviations - as opposed to frequent modestly sized deviations.
Statistical dispersion
Kurtosis
Sampling
Dependent Selection
5. 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
Null hypothesis
s-algebras
Observational study
Particular realizations of a random variable
6. 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
The Range
Statistical dispersion
A probability density function
7. ?
the population correlation
quantitative variables
Simulation
That is the median value
8. 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
P-value
Ratio measurements
Atomic event
The sample space
9. Some commonly used symbols for population parameters
applied statistics
Residuals
the population mean
Sampling frame
10. 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.
Statistical inference
Conditional distribution
Inferential statistics
Sampling
11. 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.
Statistic
Step 3 of a statistical experiment
Marginal probability
A probability distribution
12. 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.
Observational study
Block
Bias
A Statistical parameter
13. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
s-algebras
Ratio measurements
Prior probability
Outlier
14. Describes the spread in the values of the sample statistic when many samples are taken.
Statistic
Variability
covariance of X and Y
Simple random sample
15. (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.
An Elementary event
the population variance
Reliable measure
Type I errors & Type II errors
16. 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
Block
Statistical dispersion
Greek letters
Descriptive statistics
17. Is a sample space over which a probability measure has been defined.
The Expected value
A probability space
Probability density functions
Law of Parsimony
18. A measure that is relevant or appropriate as a representation of that property.
Sample space
Valid measure
A Distribution function
Ordinal measurements
19. Statistical methods can be used for summarizing or describing a collection of data; this is called
Seasonal effect
Credence
descriptive statistics
Type 2 Error
20. A consistent - repeated deviation of the sample statistic from the population parameter in the same direction when many samples are taken.
Bias
That value is the median value
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
That is the median value
21. 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
Inferential statistics
the population correlation
An estimate of a parameter
Descriptive statistics
22. Is data arising from counting that can take only non-negative integer values.
An experimental study
Count data
Independent Selection
Correlation
23. Descriptive statistics and inferential statistics (a.k.a. - predictive statistics) together comprise
applied statistics
A sample
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
hypothesis
24. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
The average - or arithmetic mean
Independent Selection
The median value
Law of Large Numbers
25. 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.
Sample space
Bias
The median value
A random variable
26. Is the study of the collection - organization - analysis - and interpretation of data. It deals with all aspects of this - including the planning of data collection in terms of the design of surveys and experiments.
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
A statistic
Statistics
Standard error
27. Where the null hypothesis fails to be rejected and an actual difference between populations is missed giving a 'false negative'.
An event
Joint probability
Divide the sum by the number of values.
Type II errors
28. When info. in a contingency table is re-organized into more or less categories - relationships seen can change or reverse.
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29. Long-term upward or downward movement over time.
Beta value
Trend
hypothesis
An estimate of a parameter
30. 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
hypothesis
A data set
Ordinal measurements
31. 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
P-value
Kurtosis
Binomial experiment
32. (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
A data set
categorical variables
expected value of X
The Expected value
33. 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.
Simpson's Paradox
Type I errors
the population cumulants
Independent Selection
34. 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.
A sampling distribution
Nominal measurements
The median value
A data set
35. 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
Probability density
Conditional distribution
Variability
Qualitative variable
36. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
Reliable measure
the population variance
Random variables
nominal - ordinal - interval - and ratio
37. Used to reduce bias - this measure weights the more relevant information higher than less relevant info.
Nominal measurements
The variance of a random variable
inferential statistics
Statistical adjustment
38. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
A Probability measure
Pairwise independence
inferential statistics
Parameter - or 'statistical parameter'
39. To find the average - or arithmetic mean - of a set of numbers:
Divide the sum by the number of values.
The median value
Posterior probability
Conditional distribution
40. Some commonly used symbols for sample statistics
Null hypothesis
Standard error
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Lurking variable
41. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.
Descriptive
Step 3 of a statistical experiment
Step 2 of a statistical experiment
Statistics
42. 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).
A Probability measure
An event
Bias
Simulation
43. 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
Placebo effect
Skewness
P-value
Divide the sum by the number of values.
44. Is data that can take only two values - usually represented by 0 and 1.
Greek letters
Binary data
Inferential statistics
Law of Parsimony
45. Any specific experimental condition applied to the subjects
nominal - ordinal - interval - and ratio
Observational study
Treatment
Standard error
46. 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
Atomic event
A likelihood function
Independent Selection
47. Is the most commonly used measure of statistical dispersion. It is the square root of the variance - and is generally written s (sigma).
The standard deviation
An Elementary event
methods of least squares
Quantitative variable
48. Are written in corresponding lower case letters. For example x1 - x2 - ... - xn could be a sample corresponding to the random variable X.
P-value
Step 1 of a statistical experiment
Particular realizations of a random variable
Probability
49. 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.
Quantitative variable
Particular realizations of a random variable
Cumulative distribution functions
That value is the median value
50. A measurement such that the random error is small
Statistic
Reliable measure
Ordinal measurements
Kurtosis