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.
William 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.
|Plot||Regular seed||Kiln-dried Seed|
We 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.
|Plot||Regular seed||Kiln-dried Seed||Difference|
Note that the differences were calculated: regular − kiln-dried.
Regular seed: regular seeds that were traditionally used for planting
kiln-dried: seed that were kiln-dried before planting
Download the seed (Links to an external site.) data file, and then upload the file into StatCrunch.
But first you will need to review the dotplots for the data (opens in a new tab).
Each link will open in a new window. To return to this discussion, either close the new tab or select the tab for this discussion.
Here is a PDF document with all StatCrunch directions (Links to an external site.).
Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.
You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.Read more
Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.Read more
Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.Read more
Your email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.Read more
By sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.Read more