1) This document provides context and data from an experiment conducted by William Gosset in 1908 to test the effects of kiln-drying seeds before planting. Gosset planted two types of seeds (regular and kiln-dried) in 11 plots to compare yields. 2) Students are asked to conduct a matched pairs t-test on the yield data using StatCrunch to test the hypothesis that kiln-dried seeds yield more corn. They must state the hypotheses, check that the data meets t-test assumptions, and report the t-score and p-value. 3) Based on the results, students should make a conclusion as to whether drying seeds before planting significantly increases yields.

1. learn by doing 2
Matched Pairs: In this lab you will learn how to conduct a matched pairs T-test for a
population mean using StatCrunch. We will work with a data set that has historical
importance in the development of the T-test.Some features of this activity may not work
well on a cell phone or tablet. We highly recommend that you complete this activity on a
computer.Here are the directions, grading rubric, and definition of high-quality feedback for
the Learn by Doing discussion board exercises.A list of StatCrunch directions is provided at
the bottom of this page.CONTEXTGOSSET’S SEED PLOT DATAWilliam S. Gosset was
employed by the Guinness brewing company of Dublin. Sample sizes available for
experimentation in brewing were necessarily small. At that time, Gosset contacted a famous
statistician Karl Pearson (1857-1936) and was told that there were no techniques for
developing probability models for small data sets. Gosset studied under Pearson, and the
outcome of his study was perhaps the most famous paper in statistical literature, “The
Probable Error of a Mean” (1908), which introduced the T-distribution.Since Gosset was
employed by Guinness, any work he produced would be owned by Guinness, so he
published under a pseudonym, “Student”; hence, the T-distribution is often referred to as
Student’s T-distribution.To illustrate his analysis, Gosset used the results of seeding 11
different plots of land with two different types of seed: regular and kiln-dried. He wanted to
determine if drying seeds before planting increased plant yield. Since different plots of soil
may be naturally more fertile, this confounding variable was eliminated by using the
matched pairs design and planting both types of seed in all 11 plots.The resulting data (corn
yield in pounds per acre) are as follows.PlotRegular seedKiln-dried
Seed1190320092193519153191020114249624635210821806196119257206021228144
4148291612154210131614431115111535We use these data to test the hypothesis that
kiln-dried seed yields more corn than regular seed.Because of the nature of the
experimental design (matched pairs), we are testing the difference in yield.PlotRegular
seedKiln-dried
SeedDifference1190316092942193519152031910161129942496246333521082180–7
261961192536716602122-
462814441482–38916121542701013161443–1271115111535–24Note that the
differences were calculated: regular − kiln-dried.VARIABLESRegular seed: regular seeds
that were traditionally used for plantingkiln-dried: seed that were kiln-dried before
plantingDATADownload the seed (Links to an external site.) data file, and then upload the
file into StatCrunch.PROMPTState the hypotheses and define the parameter.Checking

2. conditions: Since Gosset invented the T-distribution, we will assume that his sample meets
the conditions and proceed with the T-test. Regardless, answer these questions to
demonstrate your understanding of the conditions for use of the T-model.But first you will
need to review the dotplots for the data (opens in a new tab). Which graph is used to check
conditions? Why?What do we look for in the graph to verify that conditions are met?What
else do we need to know about the sample of seeds before using the T-test?Use StatCrunch
to find the T-score and the P-value. Hint: as you work through the StatCrunch directions,
keep in mind that we want to calculate the differences as regular − kiln-dried . So you will
choose Regular seed for Sample 1 and kiln-dried seed for Sample 2. (directions)Copy and
paste the information in the StatCrunch output window into your initial post.State a
conclusion based on the context of this scenario.