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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. 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






2. 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.






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






4. 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






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






6. 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






7. (e.g. ? - b) are commonly used to denote unknown parameters (population parameters).






8. 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






9. In number theory - scatter plots of data generated by a distribution function may be transformed with familiar tools used in statistics to reveal underlying patterns - which may then lead to






10. 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.






11. The proportion of the explained variation by a linear regression model in the total variation.






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






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






14. 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.


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






16. Some commonly used symbols for sample statistics






17. 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






18. 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.






19. Statistics involve methods of using information from a sample to draw conclusions regarding the population.






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






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






22. Probability of rejecting a true null hypothesis.






23. S^2






24. A measurement such that the random error is small






25. Where the null hypothesis fails to be rejected and an actual difference between populations is missed giving a 'false negative'.






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






27. 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.






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






29. 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.






30. 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






31. 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






32. 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.






33. E[X] :






34. A group of individuals sharing some common features that might affect the treatment.






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.






36. 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.






37. 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}.






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






39. (or atomic event) is an event with only one element. For example - when pulling a card out of a deck - 'getting the jack of spades' is an elementary event - while 'getting a king or an ace' is not.






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






41. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively






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. Var[X] :






44. 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.






45. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.






46. 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).






47. Is a subset of the sample space - to which a probability can be assigned. For example - on rolling a die - 'getting a five or a six' is an event (with a probability of one third if the die is fair).






48. 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.






49. 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






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