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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. The probability of correctly detecting a false null hypothesis.






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






4. 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.






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






6. 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






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






8. 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.






9. 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.






10. 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






11. 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.






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






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






14. Probability of accepting a false null hypothesis.






15. 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






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






17. 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.






18. 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.






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






20. 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.






21. 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






22. A subjective estimate of probability.






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






24. ?r






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






26. 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.






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






28. Another name for elementary event.






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






30. Any specific experimental condition applied to the subjects






31. (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.






32. Cov[X - Y] :






33. Samples are drawn from two different populations such that there is a matching of the first sample data drawn and a corresponding data value in the second sample data.






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






35. 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.






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






37. 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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38. The standard deviation of a sampling distribution.






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






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






41. 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.






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






43. 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.






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






45. 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}.






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






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






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






49. Descriptive statistics and inferential statistics (a.k.a. - predictive statistics) together comprise






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