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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. Some commonly used symbols for sample statistics






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






3. Another name for elementary event.






4. Changes over time that show a regular periodicity in the data where regular means over a fixed interval; the time between repetitions is called the period.






5. The standard deviation of a sampling distribution.






6. 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






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






8. Failing to reject a false null hypothesis.






9. A numerical measure that describes an aspect of a sample.






10. E[X] :






11. 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.






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






13. 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






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






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






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






17. 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).






18. 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).






19. Probability of accepting a false null hypothesis.






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






21. Probability of rejecting a true null hypothesis.






22. 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.






23. 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.






24. ?






25. 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






26. There are two major types of causal statistical studies: In both types of studies - the effect of differences of an independent variable (or variables) on the behavior of the dependent variable are observed. The difference between the two types lies






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






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






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






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






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






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






33. (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.






34. 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.






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






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






37. 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.






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






39. 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.






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






41. 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






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






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






44. 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.






45. 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.






46. 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.






47. 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






48. Is denoted by - pronounced 'x bar'.






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






50. 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.