Journal Article

  • The sport of Ultimate has grown from parking lot fun to international competition in its 35 year existence. As in many sports, the team that scores is subsequently on defense. Thus the probability that a team will score next is dependent on which team has scored most recently. Unlike in many other sports, teams switch ends after each score. Thus field conditions can affect the scoring patterns. The data and analyses described here can be integrated into a variety of courses ranging from introductory statistics to stochastic models.

  • Methods for calculating confidence intervals for the mean are reviewed for the case where the data come from a log-normal distribution. In a simulation study it is found that a variation of the method suggested by Cox works well in practice. An approach based on Generalized confidence intervals also works well. A comparison of our results with those of Zhou and Gao (1997) reveals that it may be preferable to base the interval on t values, rather than on z values.

  • There is a little-known but very simple generalization of the standard result that for uncorrelated random variables with common mean (mu) and variance (sigma) , the expected value of the sample variance is sigma squared . The generalization justifies the use of the usual standard error of the sample mean in possibly heteroscedastic situations, and motivates elementary estimators in even unbalanced linear random effects models. The latter both provides nontrivial examples and exercises concerning method-of-moments estimation, and also helps "demystify" the whole matter of variance component estimation. This is illustrated in general for the simple one-way context and for a specific unbalanced two-factor hierarchical data structure.

  • Testing statistical hypotheses introduces new vocabulary, concepts and a way of thinking that some students might initially find difficult. We provide a simple case that can be used in class as a gentle introduction to the ideas and procedures of hypothesis testing.

  • Typically, external assessment of school statistics concentrates on lower--level skills. This article discusses how use of the real data of CensusAtSchool makes it possible to devise questions and activities that assess deeper levels of understanding, as described in BloomÅfs Taxonomy of Cognitive Learning.

  • This article gives a flavour of the CHIME materials on data handling in Microsoft Excel. It demonstrates the facilities for data validation within Excel.

  • We derive a model, using trigonometry and the Normal distribution, for the probability that a golf putt is successful. We describe a class activity in which we lead the students through the steps of examining the data, considering possible models, constructing a probability model and checking the fit. The model is,of necessity, oversimplified, a point which the class discusses at the end of the demonstration.

  • The discussion of problems associated with the use of language, specifically vocabulary and symbolism, is extended from the teaching and learning of mathematics to the particular area of statistics.

  •  This article considers the composition of juries, asking whether this is representative of the general populations from which the juries were drawn. The binomial and hypergeometric distributions are used for probability calculations. Several example applications of both of these distributions are given, addressing racial, sex and age distributions in various cases.

  • This article shows how the birthday problem can be used to introduce the exponential distribution.

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