Chapter11_1

# Chapter11_1 - WILLIAM S GOSSET 4 Brewing Ektter Beer...

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WILLIAM S. GOSSET 4, . - -. ,'? -, Brewing Ektter Beer, Brewing New Statistics What would cause the head brewer of the famous Guinness brewery in Dublin, Ireland, not only to use statistics but to invent new statistical methods? The wch for better kr, of William Gmwt (18761937), fresh from Odord University, s a brewer in 1899. He mn became involved in experiments and in statistics to understand the data from those experiments. What are the beit varieties of barley and hops for brewing? How should they be grown, dried, and stored? The resultx of the field experiments, as you can guess, varied. Statistical inference can unmer the pa+dern behind the variation. The statistical methods available at the turn of the century ended with a version of the z test for means- even confidence intervals were not yet milable. Gosset faced the problem we noted in using the z test to introduce the rea- soning of statistical tests: he didn't know the population standard deviation a. What is more, field experiments give only small numbers of observations. Just replacing a by s in the z statistic and calling the result roughly normal wasn't accurate enough. So Cosset asked the key questian: What is the exact sam- pling distribution of the statistic (f - p)/s? By 1907 Gosset was brewer-in-charge of Guinness? experimental brewery. He also had the answer to his question and had calcula values for his new distribution. We call it the t distri- bution. The new t test identified the kt barley variety, - and Guinness promptly bought up all the available seed. Guinnes allowed Gosset to pubIish his discover- ies, but not under his own name. He used the name "Student," and the t test is sometimes called "StudentYs t" in his honor. Gossefs statistical work helped him become head brewer, a more interesting title than pro- , fmr of statistics.
616 Chapter 11 Inference for Distributions ACTIVITY 11 Paper Airplane Experiment Materials: Two paper airplane pattern sheets (in the Teacher Resource Binder), scissors, masking tape, 25-meter steel tape measure, graphing calculator The Experiment The purpose of this activity is to see which of two proto- type paper airplane models has superior flight characteristics. Specifically, the object is to determine the average distance flown for each prototype plane and to compare these average distances flown. The null hypothesis will be that there is no difference between the average distance flown by Prototype A and the average distance flown by Prototype B. So Ho: pA = pB. Equivalently, we could write Ho: pA - pB = 0. What form should the alter- native hypothesis take? (Remember that the alternative hypothesis should be stated before you conduct the experiment.) The Task Your task, as a class, is to design an experiment to determine which of the two prototype paper airplanes has the superior flight charac- teristics (i.e., flies the farthest). Then you will carry out your plan and gather the necessary data. You may want to explore the data both numerically and graphically prior to conducting formal inference. Unfortunately, we don't

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## This note was uploaded on 12/09/2011 for the course STAT 101 taught by Professor O during the Fall '08 term at Lake Land.

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Chapter11_1 - WILLIAM S GOSSET 4 Brewing Ektter Beer...

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