Estimation Principles

  • This website provides the URL of a Java applet and steps for using it. Here, students can manipulate the size of the circle and the rectangle to explore the probability that a point in the rectangle is also in the circle.
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  • This Java applet demonstrates confidence intervals for the mean. It allows the user to alter sample size, samples taken, intervals, and the option of standard error. The applet displays sample values, such as average, standard deviation, and percent covered.

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  • This article describes a dataset containing information on 308 diamond stones, which is useful when studying concepts in multiple linear regression analysis. Key Words: Categorical variables; Data transformation; Standardized residuals.
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  • This PowerPoint presentation dicusses general concepts of confidence intervals and interprets confidence intervals for a mean, difference in two means, and the relative risk. The original presenation is available for download.
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  • This PowerPoint lecture presenation explains confidence intervals for a mean when using a small sample. It discusses the t-distribution, compares the t-statistic to the z-statistic, and provides an example of a small sample confidence interval. The original presentation is available for download.
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  • This collection of calculators allows users to perform a number of statistical applications. Each provides background on the procedure and an example. Users can compute Descriptive Statistics and perform t-tests, Chi-square tests, Kolmogorov-Smirnov tests, Fisher's Exact Test, contingency tables, ANOVA, and regression.

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  • This general, introductory tutorial on mathematical modeling (in pdf format) is intended to provide an introduction to the correct analysis of data. It addresses, in an elementary way, those ideas that are important to the effort of distinguishing information from error. This distinction constitutes the central theme of the material described herein. Both deterministic modeling (univariate regression) as well as the (stochastic) modeling of random variables are considered, with emphasis on the latter. No attempt is made to cover every topic of relevance. Instead, attention is focussed on elucidating and illustrating core concepts as they apply to empirical data.

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  • This page contains information about the mass, mean temperature, length of day, rotation period, etc. for the planets of our solar system.
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  • Poses the following problem: Suppose there was one of six prizes inside your favorite box of cereal. Perhaps it's a pen, a plastic movie character, or a picture card. How many boxes of cereal would you expect to have to buy, to get all six prizes?

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  • Students explore the definition and interpretations of the probability of an event by investigating the long run proportion of times a sum of 8 is obtained when two balanced dice are rolled repeatedly. Making use of hand calculations, computer simulations, and descriptive techniques, students encounter the laws of large numbers in a familiar setting. By working through the exercises, students will gain a deeper understanding of the qualitative and quantitative relationships between theoretical probability and long run relative frequency. Particularly, students investigate the proximity of the relative frequency of an event to its probability and conclude, from data, the order on which the dispersion of the relative frequency diminishes. Key words: probability, law of large numbers, simulation, estimation

    Includes project file for Minitab and coding for a dice rolling simulation.

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