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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.
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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. Statistical methods can be used for summarizing or describing a collection of data; this is called
descriptive statistics
Null hypothesis
Law of Large Numbers
Variability
2. S^2
the population cumulants
Parameter - or 'statistical parameter'
the population variance
Independent Selection
3. Can refer either to a sample not being representative of the population - or to the difference between the expected value of an estimator and the true value.
A population or statistical population
Posterior probability
Bias
Placebo effect
4. Var[X] :
variance of X
Cumulative distribution functions
Coefficient of determination
Binomial experiment
5. Gives the probability distribution for a continuous random variable.
Interval measurements
A probability density function
Variable
covariance of X and Y
6. Is the probability of an event - ignoring any information about other events. The marginal probability of A is written P(A). Contrast with conditional probability.
A random variable
Law of Parsimony
Statistical inference
Marginal probability
7. 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.
Step 3 of a statistical experiment
the population mean
A Distribution function
Dependent Selection
8. A group of individuals sharing some common features that might affect the treatment.
Block
Bias
Coefficient of determination
experimental studies and observational studies.
9. 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
Probability and statistics
A sampling distribution
hypotheses
Estimator
10. The proportion of the explained variation by a linear regression model in the total variation.
Statistical adjustment
Dependent Selection
Trend
Coefficient of determination
11. Describes the spread in the values of the sample statistic when many samples are taken.
Variability
A sample
Null hypothesis
Conditional probability
12. Is denoted by - pronounced 'x bar'.
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Step 1 of a statistical experiment
Sample space
Power of a test
13. 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)
Average and arithmetic mean
the population mean
Interval measurements
Statistics
14. Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically - sometimes they are grouped together as
Probability density functions
A data point
categorical variables
nominal - ordinal - interval - and ratio
15. 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}.
Null hypothesis
The sample space
Simulation
The Expected value
16. 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.
Step 2 of a statistical experiment
A probability distribution
An experimental study
Ordinal measurements
17. A numerical measure that assesses the strength of a linear relationship between two variables.
An estimate of a parameter
Correlation coefficient
Inferential
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
18. A data value that falls outside the overall pattern of the graph.
An Elementary event
applied statistics
Quantitative variable
Outlier
19. 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.
Estimator
Step 3 of a statistical experiment
Statistical inference
Type 1 Error
20. A scale that represents an ordinal scale such as looks on a scale from 1 to 10.
the population cumulants
A probability space
descriptive statistics
Likert scale
21. Statistics involve methods of using information from a sample to draw conclusions regarding the population.
Random variables
Inferential
the population cumulants
Descriptive statistics
22. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.
Joint distribution
Variability
An estimate of a parameter
A likelihood function
23. Occurs when a subject receives no treatment - but (incorrectly) believes he or she is in fact receiving treatment and responds favorably.
Observational study
Placebo effect
The standard deviation
Statistic
24. When you have two or more competing models - choose the simpler of the two models.
the population correlation
Law of Parsimony
Treatment
Experimental and observational studies
25. 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.
Lurking variable
Joint distribution
Variability
applied statistics
26. 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
Observational study
Particular realizations of a random variable
the population mean
variance of X
27. Describes a characteristic of an individual to be measured or observed.
Step 1 of a statistical experiment
Random variables
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Variable
28. Of a group of numbers is the center point of all those number values.
The average - or arithmetic mean
A probability density function
Likert scale
Law of Parsimony
29. 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.
the population mean
A population or statistical population
Conditional distribution
s-algebras
30. 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.
A likelihood function
inferential statistics
A population or statistical population
Marginal probability
31. Have no meaningful rank order among values.
Marginal distribution
Nominal measurements
Standard error
Descriptive
32. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
hypotheses
nominal - ordinal - interval - and ratio
Lurking variable
Descriptive
33. 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.
Bias
Statistical dispersion
Statistics
the population mean
34. 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.
Nominal measurements
Descriptive statistics
Experimental and observational studies
Type I errors & Type II errors
35. 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.
Law of Parsimony
Law of Large Numbers
A random variable
s-algebras
36. (pdfs) and probability mass functions are denoted by lower case letters - e.g. f(x).
covariance of X and Y
Correlation coefficient
Probability density functions
Sample space
37. Some commonly used symbols for sample statistics
descriptive statistics
Type I errors & Type II errors
Likert scale
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
38. A subjective estimate of probability.
Joint probability
Step 3 of a statistical experiment
Correlation
Credence
39. Where the null hypothesis fails to be rejected and an actual difference between populations is missed giving a 'false negative'.
hypotheses
Type II errors
Standard error
Residuals
40. (or multivariate random variable) is a vector whose components are random variables on the same probability space.
observational study
Atomic event
A Random vector
Step 3 of a statistical experiment
41. 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
Step 3 of a statistical experiment
The Range
Inferential statistics
Quantitative variable
42. 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.
Type 2 Error
Binomial experiment
Null hypothesis
Marginal distribution
43. ?
hypotheses
Step 1 of a statistical experiment
the population correlation
Qualitative variable
44. The result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data
Correlation coefficient
The Expected value
The median value
Posterior probability
45. 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
P-value
Null hypothesis
A Statistical parameter
A probability distribution
46. The standard deviation of a sampling distribution.
Standard error
A sampling distribution
Type I errors & Type II errors
Divide the sum by the number of values.
47. When there is an even number of values...
nominal - ordinal - interval - and ratio
Lurking variable
Outlier
That is the median value
48. 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 Range
Atomic event
Statistics
49. Patterns in the data may be modeled in a way that accounts for randomness and uncertainty in the observations - and are then used for drawing inferences about the process or population being studied; this is called
Variable
inferential statistics
An experimental study
Individual
50. Working from a null hypothesis two basic forms of error are recognized:
Type I errors & Type II errors
categorical variables
Atomic event
Correlation coefficient
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