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CLEP General Mathematics: Probability And Statistics

Subjects : clep, math
Instructions:
  • Answer 50 questions in 15 minutes.
  • If you are not ready to take this test, you can study here.
  • 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. Is denoted by - pronounced 'x bar'.






2. Working from a null hypothesis two basic forms of error are recognized:






3. A variable has a value or numerical measurement for which operations such as addition or averaging make sense.






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






5. 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}.






6. 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






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






8. 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.






9. 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.






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






11. 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






12. 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






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






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






15. 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.






16. Two variables such that their effects on the response variable cannot be distinguished from each other.






17. Cov[X - Y] :






18. 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






19. Another name for elementary event.






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






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






22. 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.






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






24. 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.






25. (pdfs) and probability mass functions are denoted by lower case letters - e.g. f(x).






26. Probability of rejecting a true null hypothesis.






27. 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.






28. When info. in a contingency table is re-organized into more or less categories - relationships seen can change or reverse.


29. Have both a meaningful zero value and the distances between different measurements defined; they provide the greatest flexibility in statistical methods that can be used for analyzing the data






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






31. 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.






32. (or just likelihood) is a conditional probability function considered a function of its second argument with its first argument held fixed. For example - imagine pulling a numbered ball with the number k from a bag of n balls - numbered 1 to n. Then






33. 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






34. 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.






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






36. Is a sample space over which a probability measure has been defined.






37. 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






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






39.






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






41. Some commonly used symbols for sample statistics






42. Planning the research - including finding the number of replicates of the study - using the following information: preliminary estimates regarding the size of treatment effects - alternative hypotheses - and the estimated experimental variability. Co






43. E[X] :






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






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






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






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






48. 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.






49. 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.






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