State the Hypotheses and Define the Parameter Questions

Description

GOSSET’S SEED PLOT DATA

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
1	1903	2009
2	1935	1915
3	1910	2011
4	2496	2463
5	2108	2180
6	1961	1925
7	2060	2122
8	1444	1482
9	1612	1542
10	1316	1443
11	1511	1535

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
1	1903	2009	–106
2	1935	1915	20
3	1910	2011	–101
4	2496	2463	33
5	2108	2180	–72
6	1961	1925	36
7	2060	2122	–62
8	1444	1482	–38
9	1612	1542	70
10	1316	1443	–127
11	1511	1535	–24

Note that the differences were calculated: regular − kiln-dried.

Variables

Regular seed: regular seeds that were traditionally used for planting
kiln-dried: seed that were kiln-dried before planting

Prompt

1. State the hypotheses and define the parameter.
2. Checking 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).
   1. Which graph is used to check conditions? Why?
   2. What do we look for in the graph to verify that conditions are met?
   3. What else do we need to know about the sample of seeds before using the T-test?
3. 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.
4. State a conclusion based on the context of this scenario.

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