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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.
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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 a sample and the associated data points.
A data set
The Covariance between two random variables X and Y - with expected values E(X) =
Residuals
A random variable
2. Is denoted by - pronounced 'x bar'.
A Statistical parameter
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
the population variance
Quantitative variable
3. Long-term upward or downward movement over time.
Trend
Bias
Null hypothesis
An Elementary event
4. Used to reduce bias - this measure weights the more relevant information higher than less relevant info.
Statistical adjustment
A Random vector
Skewness
Statistical dispersion
5. When there is an even number of values...
Variable
observational study
That is the median value
Statistic
6. Another name for elementary event.
the population variance
Probability
descriptive statistics
Atomic event
7. Are usually written with upper case calligraphic (e.g. F for the set of sets on which we define the probability P)
A data set
hypotheses
s-algebras
The average - or arithmetic mean
8. Data are gathered and correlations between predictors and response are investigated.
A statistic
A sample
observational study
Variability
9. Have imprecise differences between consecutive values - but have a meaningful order to those values
Statistical adjustment
Divide the sum by the number of values.
the sample or population mean
Ordinal measurements
10. Probability of rejecting a true null hypothesis.
The average - or arithmetic mean
Descriptive
Joint probability
Alpha value (Level of Significance)
11. 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
the population mean
Descriptive statistics
the sample or population mean
A random variable
12. ?r
the population cumulants
covariance of X and Y
That is the median value
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
13. Given two random variables X and Y - the joint distribution of X and Y is the probability distribution of X and Y together.
Credence
A Random vector
A sample
Joint distribution
14. Descriptive statistics and inferential statistics (a.k.a. - predictive statistics) together comprise
Joint distribution
Type I errors & Type II errors
applied statistics
expected value of X
15. Is the most commonly used measure of statistical dispersion. It is the square root of the variance - and is generally written s (sigma).
methods of least squares
nominal - ordinal - interval - and ratio
Placebo effect
The standard deviation
16. Error also refers to the extent to which individual observations in a sample differ from a central value - such as
A Probability measure
A data point
the sample or population mean
Kurtosis
17. 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
A probability distribution
Observational study
An Elementary event
Probability density
18. 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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19. Have both a meaningful zero value and the distances between different measurements defined; they provide the greatest flexibility in statistical methods that can be used for analyzing the data
Ratio measurements
Cumulative distribution functions
Marginal distribution
Outlier
20. A consistent - repeated deviation of the sample statistic from the population parameter in the same direction when many samples are taken.
Posterior probability
A Probability measure
Bias
A population or statistical population
21. 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
the sample or population mean
hypothesis
Step 3 of a statistical experiment
Joint probability
22. Two variables such that their effects on the response variable cannot be distinguished from each other.
the population variance
A probability space
Confounded variables
Inferential statistics
23. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively
Ordinal measurements
Joint probability
Individual
Residuals
24. ?
the population correlation
Credence
experimental studies and observational studies.
Sampling
25. 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
A Random vector
Variable
Inferential statistics
Nominal measurements
26. 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.
Law of Large Numbers
Experimental and observational studies
Ordinal measurements
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
27. A variable describes an individual by placing the individual into a category or a group.
Statistics
Qualitative variable
descriptive statistics
Valid measure
28. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.
Sampling frame
Lurking variable
Descriptive
Variable
29. A numerical measure that describes an aspect of a population.
Parameter
The sample space
Parameter - or 'statistical parameter'
A Distribution function
30. Many statistical methods seek to minimize the mean-squared error - and these are called
quantitative variables
methods of least squares
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Independence or Statistical independence
31. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
f(z) - and its cdf by F(z).
Binary data
Law of Large Numbers
observational study
32. A scale that represents an ordinal scale such as looks on a scale from 1 to 10.
Likert scale
Bias
Marginal distribution
Simple random sample
33. (cdfs) are denoted by upper case letters - e.g. F(x).
Cumulative distribution functions
Conditional distribution
Simpson's Paradox
Confounded variables
34. S^2
Probability density
Statistics
the population variance
Joint distribution
35. Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically - sometimes they are grouped together as
Parameter
Probability density
categorical variables
Law of Large Numbers
36. A numerical measure that describes an aspect of a sample.
Likert scale
Statistic
Law of Parsimony
Quantitative variable
37. 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.
the population correlation
the population mean
A random variable
Joint probability
38. Describes the spread in the values of the sample statistic when many samples are taken.
Variability
A statistic
An estimate of a parameter
Type 1 Error
39. Are written in corresponding lower case letters. For example x1 - x2 - ... - xn could be a sample corresponding to the random variable X.
Count data
Particular realizations of a random variable
Estimator
A data set
40. Failing to reject a false null hypothesis.
Type 2 Error
Mutual independence
applied statistics
Kurtosis
41. 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
Step 2 of a statistical experiment
Standard error
experimental studies and observational studies.
nominal - ordinal - interval - and ratio
42. 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.
The variance of a random variable
categorical variables
Mutual independence
Type I errors
43. Occurs when a subject receives no treatment - but (incorrectly) believes he or she is in fact receiving treatment and responds favorably.
Type II errors
Placebo effect
observational study
Atomic event
44. 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
Count data
Type II errors
Correlation
A Statistical parameter
45. Is the probability distribution - under repeated sampling of the population - of a given statistic.
Marginal distribution
methods of least squares
Type I errors & Type II errors
A sampling distribution
46. Is its expected value. The mean (or sample mean of a data set is just the average value.
The Mean of a random variable
the population mean
expected value of X
An Elementary event
47. 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.
Confounded variables
Conditional distribution
Pairwise independence
A Distribution function
48. Have no meaningful rank order among values.
A Statistical parameter
Nominal measurements
Step 2 of a statistical experiment
The Range
49. (also called statistical variability) is a measure of how diverse some data is. It can be expressed by the variance or the standard deviation.
Marginal probability
Statistical dispersion
Interval measurements
the population mean
50. Working from a null hypothesis two basic forms of error are recognized:
Inferential statistics
s-algebras
Pairwise independence
Type I errors & Type II errors