Progress Check
Use this activity to assess whether you and your peers can:
Unde
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.
Directions
Use the drop-down menu to learn about the three steps needed to complete this assignment.
Three steps to complete the assignment
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 AcrePlotRegular seedKiln-dried Seed
119032009
219351915
319102011
424962463
521082180
619611925
720602122
814441482
916121542
1013161443
1115111535
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 YieldPlotRegular seedKiln-dried SeedDifference
119032009–106
21935191520
319102011–101
42496246333
521082180–72
61961192536
720602122–62
814441482–38
91612154270
1013161443–127
1115111535–24
Note that the differences were calculated: regular − kiln-dried.
Variables
Regular seed: regular seeds that were traditionally used for planting
Kiln-dried seed: seeds that were kiln-dried before planting
Data
Open the seeds datafile in the Stats at Cuyamaca College group on StatCrunch (directions – opens in a new tab).
Prompt
State the hypotheses and define the parameter.
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).
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 the information in the StatCrunch output window and paste it into the textbook with your response.
State a conclusion based on the context of this scenario.
List of StatCrunch Directions
Click here for StatCrunch Directions
Module 22 Discussion Board
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Content by Cuyamaca College math faculty and licensed under the Creative Commons 4.0 International LicenseLinks to an external site..
Rubric
Formative Assessments w/ StatCrunch
Formative Assessments w/ StatCrunch
CriteriaRatingsPts
This criterion is linked to a Learning OutcomeAnswering the Prompt
8 ptsFull 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 ptsMostly 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 ptsOne 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 ptsNo 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 ptsFull Credit
StatCrunch graphs and/or tables are correct and embedded with your work.
1 ptsPartial Credit
StatCrunch graphs and/or tables are incorrect or missing important information.
0 ptsNo Credit
No StatCrunch information is embedded with your post. Or all StatCrunch work is incorrect.
2 pts
Total Points: 10
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