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CLEP General Mathematics: Probability And Statistics

Subjects : clep, 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. 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






2. 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






3. 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.






4. Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically - sometimes they are grouped together as






5. A numerical measure that describes an aspect of a sample.






6. Consists of a number of independent trials repeated under identical conditions. On each trial - there are two possible outcomes.






7. Error also refers to the extent to which individual observations in a sample differ from a central value - such as






8. Is a parameter that indexes a family of probability distributions.






9. Probability of accepting a false null hypothesis.






10. Is the probability distribution - under repeated sampling of the population - of a given statistic.






11. Changes over time that show a regular periodicity in the data where regular means over a fixed interval; the time between repetitions is called the period.






12. Where the null hypothesis is falsely rejected giving a 'false positive'.






13. When you have two or more competing models - choose the simpler of the two models.






14. S^2






15. Some commonly used symbols for sample statistics






16. Of a group of numbers is the center point of all those number values.






17. (also called statistical variability) is a measure of how diverse some data is. It can be expressed by the variance or the standard deviation.






18. Many statistical methods seek to minimize the mean-squared error - and these are called






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.






20. 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.






21. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.






22. Cov[X - Y] :






23. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.






24. Describes a characteristic of an individual to be measured or observed.






25. Is inference about a population from a random sample drawn from it or - more generally - about a random process from its observed behavior during a finite period of time.






26. 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.






27. In particular - the pdf of the standard normal distribution is denoted by






28. A consistent - repeated deviation of the sample statistic from the population parameter in the same direction when many samples are taken.






29. Is defined as the expected value of random variable (X -






30. 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.






31. 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.






32. Is its expected value. The mean (or sample mean of a data set is just the average value.






33. Is data that can take only two values - usually represented by 0 and 1.






34. A measurement such that the random error is small






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






36. (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






37. Statistical methods can be used for summarizing or describing a collection of data; this is called






38. (cdfs) are denoted by upper case letters - e.g. F(x).






39. 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.






40. E[X] :






41. Failing to reject a false null hypothesis.






42. 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.






43. Is the most commonly used measure of statistical dispersion. It is the square root of the variance - and is generally written s (sigma).






44. A sample selected in such a way that each individual is equally likely to be selected as well as any group of size n is equally likely to be selected.






45. 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






46. Occurs when a subject receives no treatment - but (incorrectly) believes he or she is in fact receiving treatment and responds favorably.






47. The collection of all possible outcomes in an experiment.






48. The result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data






49. 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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50. The probability of correctly detecting a false null hypothesis.