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CLEP General Mathematics: Probability And Statistics
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clep
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math
Instructions:
Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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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. Any specific experimental condition applied to the subjects
Simple random sample
Average and arithmetic mean
Treatment
The variance of a random variable
2. Statistics involve methods of using information from a sample to draw conclusions regarding the population.
Inferential
Variable
Simulation
hypotheses
3. In particular - the pdf of the standard normal distribution is denoted by
f(z) - and its cdf by F(z).
Skewness
Outlier
methods of least squares
4. Rejecting a true null hypothesis.
Type 1 Error
Conditional probability
Block
Independence or Statistical independence
5. 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
Posterior probability
Step 2 of a statistical experiment
A likelihood function
Bias
6. Probability of rejecting a true null hypothesis.
Parameter
A probability space
Alpha value (Level of Significance)
Independent Selection
7. 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.
Type II errors
expected value of X
Joint probability
Dependent Selection
8. Is the most commonly used measure of statistical dispersion. It is the square root of the variance - and is generally written s (sigma).
An Elementary event
observational study
Type 1 Error
The standard deviation
9. 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
The average - or arithmetic mean
inferential statistics
expected value of X
Probability and statistics
10. 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.
Skewness
The sample space
Nominal measurements
The variance of a random variable
11. Is the length of the smallest interval which contains all the data.
Bias
The Range
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Conditional probability
12. Some commonly used symbols for population parameters
Experimental and observational studies
the population mean
Joint distribution
Bias
13. 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
Mutual independence
Credence
A probability density function
The average - or arithmetic mean
14. Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically - sometimes they are grouped together as
categorical variables
descriptive statistics
the population cumulants
Posterior probability
15. Is data arising from counting that can take only non-negative integer values.
A sample
Count data
Correlation
P-value
16. A variable describes an individual by placing the individual into a category or a group.
Kurtosis
the population mean
Lurking variable
Qualitative variable
17. (e.g. ? - b) are commonly used to denote unknown parameters (population parameters).
Law of Parsimony
Greek letters
quantitative variables
Quantitative variable
18. Changes over time that show a regular periodicity in the data where regular means over a fixed interval; the time between repetitions is called the period.
P-value
Seasonal effect
Treatment
Type II errors
19. A consistent - repeated deviation of the sample statistic from the population parameter in the same direction when many samples are taken.
Conditional distribution
Quantitative variable
The Range
Bias
20. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
Descriptive
Likert scale
Pairwise independence
P-value
21. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.
An estimate of a parameter
Variable
Statistical dispersion
Confounded variables
22. 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
Nominal measurements
observational study
Skewness
The variance of a random variable
23. Have imprecise differences between consecutive values - but have a meaningful order to those values
Qualitative variable
A probability distribution
Ordinal measurements
Sampling Distribution
24. 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.
Estimator
Law of Large Numbers
A population or statistical population
A data set
25. The objects described by a set of data: person (animal) - place - and - thing. (SUBJECTS)
the sample or population mean
Individual
Prior probability
Simple random sample
26. Is that part of a population which is actually observed.
A sample
Simpson's Paradox
expected value of X
Type 1 Error
27. Of a group of numbers is the center point of all those number values.
Observational study
P-value
The average - or arithmetic mean
Statistical adjustment
28. A scale that represents an ordinal scale such as looks on a scale from 1 to 10.
A probability space
Interval measurements
Beta value
Likert scale
29. Is the probability distribution - under repeated sampling of the population - of a given statistic.
A sampling distribution
Correlation coefficient
Statistic
The sample space
30. S^2
the population variance
P-value
Qualitative variable
The variance of a random variable
31. Statistical methods can be used for summarizing or describing a collection of data; this is called
descriptive statistics
A statistic
The Range
Cumulative distribution functions
32. 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
Descriptive statistics
Step 3 of a statistical experiment
Simpson's Paradox
Conditional distribution
33. Probability of accepting a false null hypothesis.
Beta value
Confounded variables
Step 1 of a statistical experiment
Statistical adjustment
34. 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
Descriptive statistics
A probability density function
Sampling Distribution
Null hypothesis
35. Another name for elementary event.
Valid measure
Atomic event
A Statistical parameter
the population correlation
36. 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.
Ratio measurements
Experimental and observational studies
s-algebras
Null hypothesis
37. ?r
the population cumulants
A Probability measure
Beta value
Reliable measure
38. Gives the probability of events in a probability space.
the sample or population mean
the population cumulants
Interval measurements
A Probability measure
39. Descriptive statistics and inferential statistics (a.k.a. - predictive statistics) together comprise
A Distribution function
Individual
applied statistics
Beta value
40. (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.
Observational study
An Elementary event
Type II errors
Interval measurements
41. Are written in corresponding lower case letters. For example x1 - x2 - ... - xn could be a sample corresponding to the random variable X.
Simulation
Atomic event
Conditional probability
Particular realizations of a random variable
42. Some commonly used symbols for sample statistics
applied statistics
Law of Parsimony
Bias
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
43. 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
Statistics
Probability density functions
Statistic
44. Are usually written in upper case roman letters: X - Y - etc.
Random variables
The Range
Probability and statistics
expected value of X
45. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively
Residuals
the population cumulants
Pairwise independence
Divide the sum by the number of values.
46. Long-term upward or downward movement over time.
Step 2 of a statistical experiment
Correlation coefficient
Trend
Qualitative variable
47. Is a parameter that indexes a family of probability distributions.
A Statistical parameter
An event
Reliable measure
Sampling Distribution
48. 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.
Sampling
An estimate of a parameter
Kurtosis
experimental studies and observational studies.
49. 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).
Cumulative distribution functions
Trend
An event
The sample space
50. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
Pairwise independence
Law of Large Numbers
Parameter - or 'statistical parameter'
the sample or population mean
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