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






3. Is a sample and the associated data points.






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






5. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.






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






7. Var[X] :






8. Some commonly used symbols for sample statistics






9. Describes the spread in the values of the sample statistic when many samples are taken.






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






11. 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.






12. 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.






13. E[X] :






14. 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.






15. Gives the probability distribution for a continuous random variable.






16. 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.






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. 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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20. Some commonly used symbols for population parameters






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






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






23. Are usually written with upper case calligraphic (e.g. F for the set of sets on which we define the probability P)






24. 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.






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






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






27. ?r






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






29. S^2






30. (or expectation) of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by its payoff ('value'). Thus - it represents the average amount one 'expects' to win per bet if bets with identical odds are re






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






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






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






34. 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






35. Used to reduce bias - this measure weights the more relevant information higher than less relevant info.






36. 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.






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






38. 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






39. 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






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






41. Have imprecise differences between consecutive values - but have a meaningful order to those values






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






43. 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






44. 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






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






46. Describes a characteristic of an individual to be measured or observed.






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






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






49. ?






50. (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