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Interpretation of Confidence Levels

  • A cartoon for teaching that confidence intervals do not always contain the true parameter. Cartoon by John Landers (www.landers.co.uk) based on an idea from Dennis Pearl (The Ohio State University). Free to use in the classroom and on course web sites.
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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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  • 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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  • The Food and Drug Administration requires pharmaceutical companies to establish a shelf life for all new drug products through a stability analysis. This is done to ensure the quality of the drug taken by an individual is within established levels. The purpose of this out-of-class project or in-class example is to determine the shelf life of a new drug. This is done through using simple linear regression models and correctly interpreting confidence and prediction intervals. An Excel spreadsheet and SAS program are given to help perform the analysis. Key words: prediction interval, confidence interval, stability

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  • The applet allows users to sample from a normal distribution or from a uniform distribution. It shows the expected values and the observed values and computes the deviation. Then, a chi-square test shows if the deviations are significant for both the normal and uniform distributions.
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