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Week 2 Guidance

# Week 2 Guidance - Week 2 Guidance Student t Distribution...

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Week 2 Guidance – Student “t” Distribution Some years ago the Guinness Brewery had a problem for which they required a creative solution. Their beer was brewed and filled into small kegs that could be more easily loaded onto the horse drawn wagons. The brewing process would continue in the smaller kegs until the ingredients required for fermentation exhausted themselves. The introduction of air into the process stopped the fermentation and thus significantly altered the product quality. Rising to the occasion, William Gossett, who was the director of quality control, needed to find a way to conduct a statistical test without sampling 30 or more kegs. (Thirty kegs represented a large portion of the batch) He began looking for some way that he could maintain reasonable statistical accuracy and reduce the number in the sample and thus reduce the cost and burden of sampling 30. He knew that if he was to use the “z” statistic as his test statistic, continuing to sample at a level of 30 to do so, that he would be using the most precise test but would continue to loose much of the companies production. He had a dilemma. Mr. Gossett needed to find a distribution that would allow him to trade sample size for precision. He had a second problem in that Guinness Brewery had a policy that employees could not publish work under their own name. Mr. Gossett developed a distribution that depends on the degrees of freedom in the sample (the number in the sample minus 1). This family of distributions are normal distributions that allow sampling at very small numbers. The solution to the second problem was solved by writing under the name “Student”. Hence we have the Student “t”. If you take a moment to look at the “t” distribution

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Week 2 Guidance - Week 2 Guidance Student t Distribution...

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