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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. Descriptive statistics and inferential statistics (a.k.a. - predictive statistics) together comprise
Lurking variable
applied statistics
Probability density functions
variance of X
2. A variable that has an important effect on the response variable and the relationship among the variables in a study but is not one of the explanatory variables studied either because it is unknown or not measured.
Step 2 of a statistical experiment
Sample space
Observational study
Lurking variable
3. Where the null hypothesis is falsely rejected giving a 'false positive'.
expected value of X
Correlation coefficient
Type I errors
A Distribution function
4. The proportion of the explained variation by a linear regression model in the total variation.
A likelihood function
Probability density functions
Coefficient of determination
Estimator
5. Is the probability of some event A - assuming event B. Conditional probability is written P(A|B) - and is read 'the probability of A - given B'
Treatment
Conditional probability
P-value
A probability space
6. 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
Confounded variables
Step 2 of a statistical experiment
Sampling Distribution
7. 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
Prior probability
Parameter - or 'statistical parameter'
Statistic
8. Are simply two different terms for the same thing. Add the given values
Average and arithmetic mean
descriptive statistics
A sampling distribution
Sample space
9. Long-term upward or downward movement over time.
A random variable
Trend
Skewness
experimental studies and observational studies.
10. 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.
s-algebras
Sampling
Marginal distribution
covariance of X and Y
11. Is the most commonly used measure of statistical dispersion. It is the square root of the variance - and is generally written s (sigma).
Binary data
A statistic
The standard deviation
A Probability measure
12. 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.
Experimental and observational studies
s-algebras
Variability
A population or statistical population
13. Var[X] :
The Range
variance of X
Posterior probability
Greek letters
14. Error also refers to the extent to which individual observations in a sample differ from a central value - such as
the sample or population mean
Statistical inference
Correlation
Seasonal effect
15. Ratio and interval measurements which can be either discrete or continuous - due to their numerical nature are grouped together as
Qualitative variable
Observational study
quantitative variables
expected value of X
16. ?r
The average - or arithmetic mean
An event
Binary data
the population cumulants
17. Failing to reject a false null hypothesis.
Lurking variable
A population or statistical population
Type 2 Error
Cumulative distribution functions
18. Many statistical methods seek to minimize the mean-squared error - and these are called
A data set
methods of least squares
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
applied statistics
19. A data value that falls outside the overall pattern of the graph.
Outlier
The variance of a random variable
applied statistics
Sampling frame
20. Is data that can take only two values - usually represented by 0 and 1.
Correlation
An Elementary event
Binary data
Step 3 of a statistical experiment
21. (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
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Correlation
applied statistics
A likelihood function
22. 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
Outlier
The Mean of a random variable
hypothesis
A probability space
23. Data are gathered and correlations between predictors and response are investigated.
the population mean
observational study
Standard error
Posterior probability
24. A subjective estimate of probability.
Type I errors
Credence
Likert scale
A Random vector
25. A consistent - repeated deviation of the sample statistic from the population parameter in the same direction when many samples are taken.
A statistic
methods of least squares
Bias
Independence or Statistical independence
26. Consists of a number of independent trials repeated under identical conditions. On each trial - there are two possible outcomes.
Parameter - or 'statistical parameter'
Binomial experiment
Greek letters
Credence
27. When you have two or more competing models - choose the simpler of the two models.
Particular realizations of a random variable
Law of Parsimony
An event
Simple random sample
28. 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.
Dependent Selection
Statistical dispersion
Treatment
Sampling frame
29. A scale that represents an ordinal scale such as looks on a scale from 1 to 10.
A likelihood function
Standard error
Likert scale
Descriptive statistics
30. 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.
Independence or Statistical independence
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Correlation
Kurtosis
31. 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
Average and arithmetic mean
experimental studies and observational studies.
Independence or Statistical independence
A probability space
32. Working from a null hypothesis two basic forms of error are recognized:
Type I errors & Type II errors
Law of Parsimony
An event
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
33. Is a sample space over which a probability measure has been defined.
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
A probability space
Pairwise independence
f(z) - and its cdf by F(z).
34. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
Law of Large Numbers
inferential statistics
Pairwise independence
methods of least squares
35. Another name for elementary event.
Law of Parsimony
Joint probability
Atomic event
Dependent Selection
36. Is data arising from counting that can take only non-negative integer values.
Count data
Marginal distribution
Parameter - or 'statistical parameter'
A Distribution function
37. Probability of rejecting a true null hypothesis.
Pairwise independence
Quantitative variable
Sampling frame
Alpha value (Level of Significance)
38. 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.
Pairwise independence
Step 2 of a statistical experiment
The variance of a random variable
Probability
39. To find the average - or arithmetic mean - of a set of numbers:
A random variable
Ordinal measurements
Divide the sum by the number of values.
Alpha value (Level of Significance)
40. Is used in 'mathematical statistics' (alternatively - 'statistical theory') to study the sampling distributions of sample statistics and - more generally - the properties of statistical procedures. The use of any statistical method is valid when the
A population or statistical population
Probability
A Probability measure
covariance of X and Y
41. Rejecting a true null hypothesis.
Reliable measure
Type 1 Error
inferential statistics
Outlier
42. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
expected value of X
Power of a test
Prior probability
A sampling distribution
43. Is its expected value. The mean (or sample mean of a data set is just the average value.
Kurtosis
Particular realizations of a random variable
Ordinal measurements
The Mean of a random variable
44. 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.
Ordinal measurements
The median value
Variability
categorical variables
45. Some commonly used symbols for population parameters
Divide the sum by the number of values.
categorical variables
the population mean
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
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
Skewness
Pairwise independence
A statistic
hypotheses
47. 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
Marginal probability
Posterior probability
Observational study
A Probability measure
48. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
Probability density
Posterior probability
variance of X
P-value
49. Any specific experimental condition applied to the subjects
Treatment
observational study
Credence
That is the median value
50. A numerical measure that describes an aspect of a population.
Sample space
Standard error
Parameter
A random variable
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