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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. Rejecting a true null hypothesis.






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






3. 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.






4. A data value that falls outside the overall pattern of the graph.






5. Some commonly used symbols for sample statistics






6. Var[X] :






7. Is that part of a population which is actually observed.






8. 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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9. A list of individuals from which the sample is actually selected.






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






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






12. 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}.






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






14. Cov[X - Y] :






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






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






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






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






19. 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






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






21. Given two random variables X and Y - the joint distribution of X and Y is the probability distribution of X and Y together.






22. 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






23. (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






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






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






26. 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.






27. 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






28. 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.






29. Is a sample and the associated data points.






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






31. 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.






32. Summarize the population data by describing what was observed in the sample numerically or graphically. Numerical descriptors include mean and standard deviation for continuous data types (like heights or weights) - while frequency and percentage are






33. 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).






34. S^2






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






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






37. 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






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






39. ?






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






41. 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.






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






43. 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.






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






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






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






47. 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.






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






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. Probability of rejecting a true null hypothesis.