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Test your basic knowledge |
CLEP General Mathematics: Probability And Statistics
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clep
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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. The proportion of the explained variation by a linear regression model in the total variation.
The variance of a random variable
An experimental study
A data point
Coefficient of determination
2. Is defined as the expected value of random variable (X -
The Mean of a random variable
The Covariance between two random variables X and Y - with expected values E(X) =
Average and arithmetic mean
A data set
3. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively
Residuals
Type I errors
the population correlation
Sampling frame
4. Have no meaningful rank order among values.
Independent Selection
inferential statistics
the population mean
Nominal measurements
5. 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.
Average and arithmetic mean
That value is the median value
Interval measurements
P-value
6. 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.
The average - or arithmetic mean
applied statistics
Standard error
A population or statistical population
7. The result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data
Sampling Distribution
Probability
Posterior probability
Simulation
8. Is a typed measurement - it can be a boolean value - a real number - a vector (in which case it's also called a data vector) - etc.
A data point
Conditional probability
Sampling
A probability distribution
9. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.
Beta value
A Distribution function
The sample space
An estimate of a parameter
10. Is that part of a population which is actually observed.
Simple random sample
Statistical adjustment
A sample
Inferential statistics
11. Ratio and interval measurements which can be either discrete or continuous - due to their numerical nature are grouped together as
quantitative variables
Interval measurements
The median value
A Probability measure
12. 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
Binary data
Simulation
Probability density
That value is the median value
13. Some commonly used symbols for sample statistics
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Type II errors
The variance of a random variable
the sample or population mean
14. Long-term upward or downward movement over time.
Pairwise independence
Trend
Average and arithmetic mean
Skewness
15. Data are gathered and correlations between predictors and response are investigated.
Conditional probability
hypothesis
Descriptive statistics
observational study
16. Is the result of applying a statistical algorithm to a data set. It can also be described as an observable random variable.
the population correlation
A statistic
Probability
Experimental and observational studies
17. 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
Random variables
Null hypothesis
Block
f(z) - and its cdf by F(z).
18. 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).
Joint probability
Confounded variables
f(z) - and its cdf by F(z).
A sampling distribution
19. 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.
Particular realizations of a random variable
Sampling
Law of Large Numbers
Correlation
20. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
A statistic
Simulation
Type I errors
P-value
21. A group of individuals sharing some common features that might affect the treatment.
A likelihood function
A probability space
Block
Statistical inference
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
Observational study
hypothesis
Mutual independence
A Distribution function
23. A variable has a value or numerical measurement for which operations such as addition or averaging make sense.
Quantitative variable
Descriptive
A Probability measure
Lurking variable
24. 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.
Atomic event
A Statistical parameter
The standard deviation
Independent Selection
25. 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.
applied statistics
Simpson's Paradox
The Range
The median value
26. The probability of correctly detecting a false null hypothesis.
hypotheses
Divide the sum by the number of values.
Power of a test
Step 3 of a statistical experiment
27. Failing to reject a false null hypothesis.
experimental studies and observational studies.
Kurtosis
Type 2 Error
Joint distribution
28. When info. in a contingency table is re-organized into more or less categories - relationships seen can change or reverse.
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29. 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.
Marginal distribution
methods of least squares
Count data
the population mean
30. Var[X] :
variance of X
The Mean of a random variable
An Elementary event
Parameter
31. Two variables such that their effects on the response variable cannot be distinguished from each other.
Prior probability
Parameter
Confounded variables
nominal - ordinal - interval - and ratio
32. Many statistical methods seek to minimize the mean-squared error - and these are called
A Statistical parameter
methods of least squares
Bias
An event
33. 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
Confounded variables
Descriptive statistics
Type II errors
A data point
34. Of a group of numbers is the center point of all those number values.
An estimate of a parameter
Skewness
A probability density function
The average - or arithmetic mean
35. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.
Type I errors
Simpson's Paradox
Statistics
Descriptive
36. 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 inference
nominal - ordinal - interval - and ratio
Simulation
37. Is a sample space over which a probability measure has been defined.
A probability space
Placebo effect
Probability density functions
Coefficient of determination
38. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
The Range
nominal - ordinal - interval - and ratio
Mutual independence
Standard error
39. 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
Experimental and observational studies
Skewness
Sampling frame
Inferential
40. 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.
Parameter - or 'statistical parameter'
A random variable
methods of least squares
A Distribution function
41. Rejecting a true null hypothesis.
Descriptive statistics
Type 1 Error
Interval measurements
Greek letters
42. (or expectation) of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by its payoff ('value'). Thus - it represents the average amount one 'expects' to win per bet if bets with identical odds are re
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
The Expected value
hypotheses
A sampling distribution
43. Where the null hypothesis fails to be rejected and an actual difference between populations is missed giving a 'false negative'.
An event
Type II errors
Statistical inference
f(z) - and its cdf by F(z).
44. 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
observational study
Conditional probability
Inferential statistics
A sample
45. To find the average - or arithmetic mean - of a set of numbers:
Divide the sum by the number of values.
P-value
Binary data
Ratio measurements
46. Gives the probability of events in a probability space.
The variance of a random variable
A Probability measure
Step 2 of a statistical experiment
Standard error
47. Gives the probability distribution for a continuous random variable.
A probability density function
Treatment
variance of X
Simulation
48. Is the probability distribution - under repeated sampling of the population - of a given statistic.
A sampling distribution
Pairwise independence
Variability
Step 2 of a statistical experiment
49. Some commonly used symbols for population parameters
the population mean
the sample or population mean
Binomial experiment
Confounded variables
50. A scale that represents an ordinal scale such as looks on a scale from 1 to 10.
Pairwise independence
Likert scale
Probability density functions
Confounded variables