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






3. 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.






4. 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






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






6. 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.






7. To find the average - or arithmetic mean - of a set of numbers:






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. Involves taking measurements of the system under study - manipulating the system - and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements.






10. A numerical measure that describes an aspect of a population.






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






12. 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.






13. 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






14. 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.






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






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






17. 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.






18. E[X] :






19. 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






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






21. 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






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






23. 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






24. The standard deviation of a sampling distribution.






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






26. A subjective estimate of probability.






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






28.






29. 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






30. 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).






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






32. (or multivariate random variable) is a vector whose components are random variables on the same probability space.






33. Uses patterns in the sample data to draw inferences about the population represented - accounting for randomness. These inferences may take the form of: answering yes/no questions about the data (hypothesis testing) - estimating numerical characteris






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






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






36. 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.






37. 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






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






39. 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






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






41. S^2






42. Is a sample and the associated data points.






43. Is the length of the smallest interval which contains all the data.






44. 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.






45. 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.






46. 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.






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






48. Failing to reject a false null hypothesis.






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






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