Lab (14 of 19) 2

Progress Check

Use this activity to assess whether you and your peers can:

• Under appropriate conditions, conduct a hypothesis test about a mean for a matched pairs design. State a conclusion in context.

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Directions

Use the drop-down menu to learn about the three steps needed to complete this assignment.

Three steps to complete the assignment

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Context

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.

Corn Yield in Pounds per Acre

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.

Differences in Corn 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.

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Variables

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

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Data

Open the seeds datafile in the Stats at Cuyamaca College group on StatCrunch (directions – opens in a new tab).

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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 the information in the StatCrunch output window and paste it into the textbook with your response.
4. State a conclusion based on the context of this scenario.

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List of StatCrunch Directions

Click here for StatCrunch Directions

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Module 22 Discussion Board

Use the Module 22 discussion board (opens in a new tab) to ask questions or provide feedback about the problems in any Module 22 activity – including this peer-reviewed assignment.

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Review Feedback

• Instructor feedback is only available after an assignment is graded.
• Use these directions (opens in a new tab) to learn how to review feedback.

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Click the “Next” or > button to continue.

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Rubric

Formative Assessments w/ StatCrunch

Formative Assessments w/ StatCrunch

Criteria	Ratings	Pts
This criterion is linked to a Learning OutcomeAnswering the Prompt	8 pts Full Credit The first submission demonstrates a good-faith effort to address each part of the Prompt. Either in the first draft or the optional final draft, all parts of the “Prompt” are addressed and the responses demonstrate attainment of the learning objectives in the “Progress Check” section of the assignment. The answers are correct. The writing/work is clear. The explanation/work is reasonable, well-organized, and easy to follow. 6.5 pts Mostly Correct The first submission demonstrates a good-faith effort to address most of the Prompt. In the optional final draft all parts of the “Prompt” are addressed, and the responses demonstrate attainment of the learning objectives in the “Progress Check” section of the assignment. The answers are mostly correct. The writing/work is clear. The explanation/work is reasonable, well-organized, and easy to follow. 3.5 pts One or more incorrect The first submission demonstrates a good-faith effort to respond to a smaller portion of the Prompt. In the first draft or the optional final draft, one or more parts of the “Prompt” are not addressed or are incorrect. Or, answers do not demonstrate attainment of the learning objectives in the “Progress Check” section of the assignment. Or, answers are correct, but the writing/work is unclear, incorrect, or difficult to follow. 0 pts No Marks The first submission does not demonstrate a good-faith effort to address the Prompt.	8 pts
This criterion is linked to a Learning OutcomeStatCrunch	2 pts Full Credit StatCrunch graphs and/or tables are correct and embedded with your work. 1 pts Partial Credit StatCrunch graphs and/or tables are incorrect or missing important information. 0 pts No Credit No StatCrunch information is embedded with your post. Or all StatCrunch work is incorrect.	2 pts
Total Points: 10