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






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






3. 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)






4. 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






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






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






7. Some commonly used symbols for sample statistics






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






9. 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






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






11. Probability of rejecting a true null hypothesis.






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. 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






14. 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






15. 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






16. A subjective estimate of probability.






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






18. 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.






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






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






21. Cov[X - Y] :






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






23. The objects described by a set of data: person (animal) - place - and - thing. (SUBJECTS)






24. Have no meaningful rank order among values.






25. 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






26. Is data arising from counting that can take only non-negative integer values.






27.






28. 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.






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






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






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






32. 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.






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






34. Is the probability of some event A - assuming event B. Conditional probability is written P(A|B) - and is read 'the probability of A - given B'






35. (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






36. Working from a null hypothesis two basic forms of error are recognized:






37. 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.






38. A numerical measure that assesses the strength of a linear relationship between two variables.






39. S^2






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






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






42. The collection of all possible outcomes in an experiment.






43. 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.






44. Are usually written in upper case roman letters: X - Y - etc.






45. 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.






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






47. Occurs when a subject receives no treatment - but (incorrectly) believes he or she is in fact receiving treatment and responds favorably.






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






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






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