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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. To find the average - or arithmetic mean - of a set of numbers:
Independent Selection
The Expected value
The Range
Divide the sum by the number of values.
2. A numerical measure that describes an aspect of a sample.
covariance of X and Y
Statistic
An estimate of a parameter
Greek letters
3. A list of individuals from which the sample is actually selected.
Sampling frame
A data set
A probability distribution
Individual
4. Descriptive statistics and inferential statistics (a.k.a. - predictive statistics) together comprise
Simpson's Paradox
Step 1 of a statistical experiment
Inferential statistics
applied statistics
5. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
The Covariance between two random variables X and Y - with expected values E(X) =
Bias
A data set
Pairwise independence
6. Is its expected value. The mean (or sample mean of a data set is just the average value.
The Mean of a random variable
Null hypothesis
A data point
Residuals
7. 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 average - or arithmetic mean
A Probability measure
Marginal distribution
A data set
8. Is the most commonly used measure of statistical dispersion. It is the square root of the variance - and is generally written s (sigma).
Random variables
The standard deviation
A Distribution function
methods of least squares
9. 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.
Statistic
Parameter - or 'statistical parameter'
A statistic
Sampling
10. Data are gathered and correlations between predictors and response are investigated.
Type 1 Error
A statistic
observational study
Bias
11. 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.
Independent Selection
The variance of a random variable
Mutual independence
Confounded variables
12. Describes a characteristic of an individual to be measured or observed.
The sample space
Variable
Coefficient of determination
Standard error
13. Cov[X - Y] :
Dependent Selection
Marginal probability
covariance of X and Y
A random variable
14. 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
Skewness
Probability
Correlation
A Distribution function
15. 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
Coefficient of determination
Statistical inference
applied statistics
Probability density
16. Two events are independent if the outcome of one does not affect that of the other (for example - getting a 1 on one die roll does not affect the probability of getting a 1 on a second roll). Similarly - when we assert that two random variables are i
Independence or Statistical independence
applied statistics
Simple random sample
Marginal probability
17. 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.
quantitative variables
The median value
hypotheses
Step 1 of a statistical experiment
18. A data value that falls outside the overall pattern of the graph.
The average - or arithmetic mean
Outlier
Lurking variable
That value is the median value
19. 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).
Bias
Joint probability
A population or statistical population
That is the median value
20. A numerical measure that describes an aspect of a population.
Particular realizations of a random variable
Valid measure
Bias
Parameter
21. E[X] :
Probability
the sample or population mean
observational study
expected value of X
22. Rejecting a true null hypothesis.
Type I errors & Type II errors
Ordinal measurements
Type 1 Error
The Expected value
23. Is that part of a population which is actually observed.
categorical variables
Variable
Null hypothesis
A sample
24. 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.
Qualitative variable
A random variable
The Covariance between two random variables X and Y - with expected values E(X) =
quantitative variables
25. 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
A sampling distribution
Variable
Treatment
26. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
Prior probability
Simulation
A sampling distribution
Trend
27. 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.
Independent Selection
Statistical inference
Cumulative distribution functions
Binary data
28. (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 adjustment
Joint distribution
Statistical dispersion
The standard deviation
29. When there is an even number of values...
Treatment
Experimental and observational studies
That is the median value
An event
30. The collection of all possible outcomes in an experiment.
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
variance of X
Sample space
Individual
31. 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.
An experimental study
A Random vector
That is the median value
A population or statistical population
32. A measure that is relevant or appropriate as a representation of that property.
Valid measure
Descriptive statistics
Treatment
That is the median value
33. 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.
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34. The proportion of the explained variation by a linear regression model in the total variation.
A Statistical parameter
A population or statistical population
Coefficient of determination
A Probability measure
35. Is a function of the known data that is used to estimate an unknown parameter; an estimate is the result from the actual application of the function to a particular set of data. The mean can be used as an estimator.
Ratio measurements
The Covariance between two random variables X and Y - with expected values E(X) =
Estimator
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
36. 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.
Statistics
A Statistical parameter
Lurking variable
A data point
37. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.
Variable
An estimate of a parameter
Average and arithmetic mean
Sample space
38. Given two random variables X and Y - the joint distribution of X and Y is the probability distribution of X and Y together.
A probability space
Law of Parsimony
A sampling distribution
Joint distribution
39. A scale that represents an ordinal scale such as looks on a scale from 1 to 10.
Likert scale
A sampling distribution
That is the median value
Lurking variable
40. 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
hypothesis
A random variable
Type I errors & Type II errors
41. Some commonly used symbols for sample statistics
Kurtosis
Seasonal effect
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
nominal - ordinal - interval - and ratio
42. Is defined as the expected value of random variable (X -
Placebo effect
Correlation
Simulation
The Covariance between two random variables X and Y - with expected values E(X) =
43. 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
A data point
Statistical adjustment
experimental studies and observational studies.
Residuals
44. A sample selected in such a way that each individual is equally likely to be selected as well as any group of size n is equally likely to be selected.
Simple random sample
descriptive statistics
Beta value
Statistical dispersion
45. 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}.
A Random vector
Likert scale
The sample space
Statistical inference
46. Are usually written with upper case calligraphic (e.g. F for the set of sets on which we define the probability P)
s-algebras
applied statistics
The Expected value
The sample space
47. Are simply two different terms for the same thing. Add the given values
Average and arithmetic mean
Nominal measurements
Joint probability
Descriptive
48. 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.
Step 3 of a statistical experiment
Joint distribution
The Expected value
Experimental and observational studies
49.
the population mean
Inferential statistics
Marginal distribution
Correlation
50. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
Law of Parsimony
The Range
Law of Large Numbers
Null hypothesis
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