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






3. 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.






4. Design of experiments - using blocking to reduce the influence of confounding variables - and randomized assignment of treatments to subjects to allow unbiased estimates of treatment effects and experimental error. At this stage - the experimenters a






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






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






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






8. 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






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






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






11. Is a set of entities about which statistical inferences are to be drawn - often based on random sampling. One can also talk about a population of measurements or values.






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






13. Have meaningful distances between measurements defined - but the zero value is arbitrary (as in the case with longitude and temperature measurements in Celsius or Fahrenheit)






14. 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






15. Rejecting a true null hypothesis.






16. Some commonly used symbols for sample statistics






17. 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.






18. 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.






19. Is a parameter that indexes a family of probability distributions.






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






21. 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






22. Interpretation of statistical information in that the assumption is that whatever is proposed as a cause has no effect on the variable being measured can often involve the development of a






23. Can refer either to a sample not being representative of the population - or to the difference between the expected value of an estimator and the true value.






24. 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).






25. Patterns in the data may be modeled in a way that accounts for randomness and uncertainty in the observations - and are then used for drawing inferences about the process or population being studied; this is called






26. Is a function that gives the probability of all elements in a given space: see List of probability distributions






27. (cdfs) are denoted by upper case letters - e.g. F(x).






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






29. 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.






30. A subjective estimate of probability.






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






33. 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.






34. Probability of accepting a false null hypothesis.






35. Is a sample and the associated data points.






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






37. 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






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






39. 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.






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






41. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.






42. ?r






43. A measurement such that the random error is small






44. 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.






45. 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






46. 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






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






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






49. 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.






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