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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. A collection of events is mutually independent if for any subset of the collection - the joint probability of all events occurring is equal to the product of the joint probabilities of the individual events. Think of the result of a series of coin-fl






2. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.






3. Failing to reject a false null hypothesis.






4. The probability of correctly detecting a false null hypothesis.






5. A numerical facsimilie or representation of a real-world phenomenon.






6. A measurement such that the random error is small






7. 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






8. Any specific experimental condition applied to the subjects






9. 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.






10. A pairwise independent collection of random variables is a set of random variables any two of which are independent.






11. Data are gathered and correlations between predictors and response are investigated.






12. 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.






13. When there is an even number of values...






14. 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






15. 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






16. 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.






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






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






19. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.






20. Is a function that gives the probability of all elements in a given space: see List of probability distributions






21. Is the result of applying a statistical algorithm to a data set. It can also be described as an observable random variable.






22. Are usually written in upper case roman letters: X - Y - etc.






23. A measure that is relevant or appropriate as a representation of that property.






24. Two events are independent if the outcome of one does not affect that of the other (for example - getting a 1 on one die roll does not affect the probability of getting a 1 on a second roll). Similarly - when we assert that two random variables are i






25. 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






26. A variable describes an individual by placing the individual into a category or a group.






27. 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.






28. Probability of accepting a false null hypothesis.






29. Are written in corresponding lower case letters. For example x1 - x2 - ... - xn could be a sample corresponding to the random variable X.






30. Cov[X - Y] :






31. S^2






32. 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'






33. 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.






34. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.






35. 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)






36. Are simply two different terms for the same thing. Add the given values






37. 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.






38. Gives the probability of events in a probability space.






39. 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.






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






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






42. 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}.






43. 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.






44. 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.






45. 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






46. 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.






47. 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.






48. 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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49. 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).






50. 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.