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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
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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. (cdfs) are denoted by upper case letters - e.g. F(x).
Binomial experiment
Cumulative distribution functions
Pairwise independence
Step 2 of a statistical experiment
2. Some commonly used symbols for population parameters
Parameter - or 'statistical parameter'
variance of X
Block
the population mean
3. 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).
Ratio measurements
Power of a test
An event
Statistical dispersion
4. 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
Statistical inference
Step 1 of a statistical experiment
The average - or arithmetic mean
The Expected value
5. A numerical facsimilie or representation of a real-world phenomenon.
Simulation
Binary data
quantitative variables
The average - or arithmetic mean
6. Is the function that gives the probability distribution of a random variable. It cannot be negative - and its integral on the probability space is equal to 1.
covariance of X and Y
A Distribution function
Inferential statistics
Individual
7. (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
The median value
The Expected value
expected value of X
Ordinal measurements
8. Is data arising from counting that can take only non-negative integer values.
Count data
Individual
A probability space
Type I errors
9. Long-term upward or downward movement over time.
Probability
Trend
methods of least squares
Correlation coefficient
10. Probability of rejecting a true null hypothesis.
Quantitative variable
Alpha value (Level of Significance)
P-value
the population mean
11. Have imprecise differences between consecutive values - but have a meaningful order to those values
Type II errors
That value is the median value
Probability
Ordinal measurements
12. In particular - the pdf of the standard normal distribution is denoted by
A probability space
Independence or Statistical independence
Pairwise independence
f(z) - and its cdf by F(z).
13. 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
Interval measurements
Experimental and observational studies
experimental studies and observational studies.
Valid measure
14. 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
Variable
The Range
Probability density
A probability density function
15. Gives the probability of events in a probability space.
Statistical adjustment
Atomic event
Simulation
A Probability measure
16. Another name for elementary event.
Atomic event
Prior probability
Correlation
categorical variables
17. A collection of events is mutually independent if for any subset of the collection - the joint probability of all events occurring is equal to the product of the joint probabilities of the individual events. Think of the result of a series of coin-fl
That is the median value
the sample or population mean
Mutual independence
Random variables
18. Is a sample and the associated data points.
Type 2 Error
observational study
experimental studies and observational studies.
A data set
19. Is its expected value. The mean (or sample mean of a data set is just the average value.
hypothesis
The variance of a random variable
Greek letters
The Mean of a random variable
20. 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 statistic
Outlier
A probability space
The variance of a random variable
21. Occurs when a subject receives no treatment - but (incorrectly) believes he or she is in fact receiving treatment and responds favorably.
The Covariance between two random variables X and Y - with expected values E(X) =
Atomic event
A random variable
Placebo effect
22. 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.
Independent Selection
Sampling
The sample space
Conditional distribution
23. Also called correlation coefficient - is a numeric measure of the strength of linear relationship between two random variables (one can use it to quantify - for example - how shoe size and height are correlated in the population). An example is the P
Type 2 Error
Conditional probability
Correlation
Trend
24. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
Probability density
A statistic
The median value
nominal - ordinal - interval - and ratio
25. Cov[X - Y] :
Step 2 of a statistical experiment
covariance of X and Y
Step 1 of a statistical experiment
A probability density function
26. Is a function that gives the probability of all elements in a given space: see List of probability distributions
Type I errors & Type II errors
A probability distribution
Confounded variables
the population variance
27. ?r
the population cumulants
Type I errors
P-value
descriptive statistics
28. 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}.
The sample space
Statistical adjustment
Probability and statistics
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
29. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
Pairwise independence
A Random vector
Type 1 Error
Null hypothesis
30. Consists of a number of independent trials repeated under identical conditions. On each trial - there are two possible outcomes.
A probability distribution
Binomial experiment
An experimental study
Independent Selection
31. A consistent - repeated deviation of the sample statistic from the population parameter in the same direction when many samples are taken.
Reliable measure
Valid measure
The Range
Bias
32. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
Law of Large Numbers
Prior probability
A population or statistical population
Parameter - or 'statistical parameter'
33. Is the result of applying a statistical algorithm to a data set. It can also be described as an observable random variable.
A statistic
Descriptive statistics
Sample space
Statistic
34. Describes the spread in the values of the sample statistic when many samples are taken.
Variability
Statistical dispersion
That value is the median value
Sampling
35. 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.
Probability density
Alpha value (Level of Significance)
A random variable
A Random vector
36. Are usually written with upper case calligraphic (e.g. F for the set of sets on which we define the probability P)
hypotheses
Experimental and observational studies
s-algebras
Placebo effect
37. 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
Simpson's Paradox
s-algebras
Probability
hypothesis
38. (e.g. ? - b) are commonly used to denote unknown parameters (population parameters).
A Random vector
Greek letters
A likelihood function
Skewness
39. The proportion of the explained variation by a linear regression model in the total variation.
Trend
That is the median value
Coefficient of determination
Statistical dispersion
40. Gives the probability distribution for a continuous random variable.
Sampling Distribution
the population cumulants
Statistical inference
A probability density function
41. The standard deviation of a sampling distribution.
Variability
f(z) - and its cdf by F(z).
Confounded variables
Standard error
42. Is the probability distribution - under repeated sampling of the population - of a given statistic.
A sampling distribution
A Random vector
Coefficient of determination
Individual
43. Are usually written in upper case roman letters: X - Y - etc.
The average - or arithmetic mean
the population cumulants
Pairwise independence
Random variables
44. 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.
Reliable measure
Coefficient of determination
Sampling
the population cumulants
45. Where the null hypothesis fails to be rejected and an actual difference between populations is missed giving a 'false negative'.
A statistic
Bias
Type II errors
The sample space
46. The result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data
Ratio measurements
Conditional probability
Posterior probability
Bias
47. 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.
the sample or population mean
Standard error
Kurtosis
That value is the median value
48. 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
categorical variables
Parameter
Variable
Probability and statistics
49. Used to reduce bias - this measure weights the more relevant information higher than less relevant info.
Parameter
Independent Selection
Trend
Statistical adjustment
50. A numerical measure that assesses the strength of a linear relationship between two variables.
Correlation coefficient
Independent Selection
Type I errors & Type II errors
Ordinal measurements