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CLEP General Mathematics: Probability And Statistics
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Instructions:
Answer 50 questions in 15 minutes.
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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 the length of the smallest interval which contains all the data.
An Elementary event
Seasonal effect
The variance of a random variable
The Range
2. A numerical measure that assesses the strength of a linear relationship between two variables.
nominal - ordinal - interval - and ratio
Interval measurements
Posterior probability
Correlation coefficient
3. 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}.
Sample space
covariance of X and Y
The sample space
Interval measurements
4. ?r
Observational study
Experimental and observational studies
the population mean
the population cumulants
5. Ratio and interval measurements which can be either discrete or continuous - due to their numerical nature are grouped together as
Sample space
An experimental study
A statistic
quantitative variables
6. A variable has a value or numerical measurement for which operations such as addition or averaging make sense.
Probability density functions
Marginal probability
The standard deviation
Quantitative variable
7. 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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8. The proportion of the explained variation by a linear regression model in the total variation.
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Type 1 Error
Coefficient of determination
Bias
9. Describes a characteristic of an individual to be measured or observed.
Ratio measurements
The variance of a random variable
Variable
A sampling distribution
10. Two variables such that their effects on the response variable cannot be distinguished from each other.
Qualitative variable
Confounded variables
A probability space
Binary data
11. Used to reduce bias - this measure weights the more relevant information higher than less relevant info.
Statistical adjustment
A Statistical parameter
Trend
Confounded variables
12. (pdfs) and probability mass functions are denoted by lower case letters - e.g. f(x).
A probability density function
Statistical adjustment
the population correlation
Probability density functions
13. Involves taking measurements of the system under study - manipulating the system - and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements.
the sample or population mean
Seasonal effect
Probability density
An experimental study
14. E[X] :
The Range
The Covariance between two random variables X and Y - with expected values E(X) =
expected value of X
f(z) - and its cdf by F(z).
15. 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.
Statistical dispersion
covariance of X and Y
Conditional probability
That value is the median value
16. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
Observational study
P-value
s-algebras
Posterior probability
17. Have meaningful distances between measurements defined - but the zero value is arbitrary (as in the case with longitude and temperature measurements in Celsius or Fahrenheit)
Random variables
Residuals
The variance of a random variable
Interval measurements
18. A measure that is relevant or appropriate as a representation of that property.
The Covariance between two random variables X and Y - with expected values E(X) =
An estimate of a parameter
Valid measure
the population correlation
19. 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.
the sample or population mean
Probability
A Distribution function
Skewness
20. 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
Mutual independence
Conditional probability
A data set
21. 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
Standard error
Probability and statistics
The standard deviation
Confounded variables
22. Are usually written with upper case calligraphic (e.g. F for the set of sets on which we define the probability P)
s-algebras
Kurtosis
nominal - ordinal - interval - and ratio
the population variance
23. The result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data
Posterior probability
Experimental and observational studies
Probability and statistics
A Random vector
24. 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.
Variability
Experimental and observational studies
the population cumulants
Law of Large Numbers
25. Where the null hypothesis fails to be rejected and an actual difference between populations is missed giving a 'false negative'.
Type II errors
Variability
Standard error
the population variance
26. 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
Confounded variables
Bias
The sample space
27. Probability of rejecting a true null hypothesis.
Experimental and observational studies
The Mean of a random variable
Binomial experiment
Alpha value (Level of Significance)
28. 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
variance of X
Binomial experiment
Simple random sample
Inferential statistics
29. The standard deviation of a sampling distribution.
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Probability
Standard error
A Probability measure
30. Where the null hypothesis is falsely rejected giving a 'false positive'.
Individual
Type I errors
Particular realizations of a random variable
Kurtosis
31. Long-term upward or downward movement over time.
Residuals
Trend
Bias
Interval measurements
32. 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.
Qualitative variable
Individual
Sampling
Prior probability
33. When you have two or more competing models - choose the simpler of the two models.
A statistic
Random variables
Step 3 of a statistical experiment
Law of Parsimony
34. (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
A likelihood function
Estimator
inferential statistics
An experimental study
35. 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
Probability density
Residuals
Step 3 of a statistical experiment
Interval measurements
36. Given two random variables X and Y - the joint distribution of X and Y is the probability distribution of X and Y together.
Average and arithmetic mean
Joint distribution
Confounded variables
Qualitative variable
37. Consists of a number of independent trials repeated under identical conditions. On each trial - there are two possible outcomes.
methods of least squares
Binomial experiment
Observational study
A sample
38. 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.
Variable
Estimator
Particular realizations of a random variable
Atomic event
39. Is a parameter that indexes a family of probability distributions.
A Statistical parameter
Inferential
Simple random sample
Variability
40. Is the result of applying a statistical algorithm to a data set. It can also be described as an observable random variable.
Descriptive
Confounded variables
categorical variables
A statistic
41. Describes the spread in the values of the sample statistic when many samples are taken.
Type I errors & Type II errors
methods of least squares
Variability
An estimate of a parameter
42. Is the probability distribution - under repeated sampling of the population - of a given statistic.
Marginal probability
Atomic event
A sampling distribution
Skewness
43. 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).
Average and arithmetic mean
An event
Reliable measure
hypothesis
44. 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
Step 2 of a statistical experiment
Probability and statistics
Pairwise independence
Observational study
45. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
Sample space
Beta value
Standard error
Prior probability
46. 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
the population cumulants
the population mean
hypotheses
Experimental and observational studies
47. A numerical facsimilie or representation of a real-world phenomenon.
Simulation
Valid measure
the population variance
An event
48. (also called statistical variability) is a measure of how diverse some data is. It can be expressed by the variance or the standard deviation.
Null hypothesis
Statistical dispersion
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Conditional probability
49. (e.g. ? - b) are commonly used to denote unknown parameters (population parameters).
s-algebras
Lurking variable
Greek letters
Dependent Selection
50. Working from a null hypothesis two basic forms of error are recognized:
Descriptive statistics
Observational study
Type I errors & Type II errors
Marginal distribution
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