matched pairs

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Learn by Doing

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.

Paired T hypothesis test:

μD = μ1 – μ2 : Mean of the difference between Regular seed and Kiln-dried seed
H0 : μD = 0
HA : μD > 0
Hypothesis test results:

Difference Mean Std. Err. DF T-Stat P-value
Regular seed – Kiln-dried seed -33.727273 19.951346 10 -1.6904761 0.9391

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.

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.

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

Data

Download the seed (Links to an external site.) data file, and then upload the file into StatCrunch.

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.

EXAMPLE TO RIGHT ANSWER

1. Ho: μ=0

Ha: μ>0

The average difference is -33.73

2. a) We use the graph of the differences because that is what we are analyzing.

b) We look to see if the graph is normally distributed, not skewed, and doesn’t have outliers.

c) We don’t know if the data is randomly selected.

3.

Paired T hypothesis test:

μD = μ1 – μ2 : Mean of the difference between Regular seed and Kiln-dried seed
H0 : μD = 0
HA : μD > 0
Hypothesis test results:

Difference Mean Std. Err. DF T-Stat P-value
Regular seed – Kiln-dried seed -33.727273 19.951346 10 -1.6904761 0.9391

Differences stored in column, Differences.

4. Based on the P-value of 0.9391, we do not have enough evidence to reject the null hypothesis. There is no statistically significant evidence to show that kiln-dried seeds yield more than regular seeds.

 

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Elk Grove Unified School District v. Newdow!

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Directions: Religion and Politics have traditional been highly debated topics in our society. Recently, the Pledge of Allegiance has added to this debate. American citizens have generally recited the Pledge of Allegiance at important ceremonies ranging from presidential inaugurations to the beginning of the school day. The pledge has a great deal of sentimental value to many Americans, but also creates a great deal of controversy for others.  
 
Review the Supreme Court case Elk Grove Unified School District v. Newdow, which highlights the debate.
 
Write a five to eight (5-8) page paper in which you:
 

Summarize the salient points of the Supreme Court case Elk Grove Unified School District v. Newdow. (Who are the people involved in this case; why did they bring this grievance to the court system; what are the important points of this case; when did this case take place—the date, meaning month day and year.)

Discuss the levels of the court through which the case evolved before it reached the Supreme Court. (Where did this case originate—in which state—and which court system did it go through—for example: Civil or Criminal—describe the various courts it went through before reaching the US Supreme Court)

Explain the decision of the Supreme Court in this case in brief. (What were the major points of the Justices?  What were some dissenting and agreeing arguments?)

Explain the fundamental impact that the court decision in question has had on American society in general and on ethics in American society in particular. Provide a rationale for the response. (Did this case change the way schools around the nation approach the Pledge of Allegiance?  Did this case change the way schools in specific states approach the Pledge of Allegiance? Meaning: did schools become cautious? Did they stop?  What did they do?  Did teachers change their behavior?  Did principals?  Find a specific school and write about their practices revolving around this issue.  BE SPECIFIC.  Do not use generalizations.  A generalization is: They are more cautious now because it was brought before the Supreme Court and they said so and so.  So and so is not CONCRETE rationale.  Concrete rationale is: According to a January 22, 2005 article in the New York Times, after the Elk Grove Unified School District v. Newdow decision, the Monroe County school district no longer makes it mandatory for students to recite the pledge of allegiance…as a result local parents were outraged.  These are just examples.)

Discuss whether you believe that the recitation of the Pledge of Allegiance is a religious issue or a sign of respect for the United States. (This is a question of religion vs. state.  This might also be a question about nationalism.  Does this case protect ones religious freedoms or oneâ€s first amendment rights?  Again be specific here, do not over generalize.  Make your point and make sure it is clearly stated.  Remember: this is a sociological question, about law, so cite the constitution if necessary.  It is not a personal question.)

Discuss whether or not you think public schools should be allowed to recite the pledge. (This is your conclusion and it is asking you for your education opinion.  Not your personal one.  Examples of educated opinion: Public schools should not be allowed to recite the pledge because it has the potential of infringing on a studentâ€s religious beliefs and can be viewed as discriminatory.  Examples of personal opinion: I think that public schools shouldnâ€t be allowed to recite the pledge of allegiance because when I was a kid it wasnâ€t a big deal and people should just get over it.  Itâ€s the American way.  And anyone who doesnâ€t agree is anti-American…etc., etc., etc.,) 

Use at least three (3) quality academic resources. Note: Wikipedia and other Websites do not qualify as academic resources.

 
 
 
Your assignment must follow these formatting requirements:
 

Be typed, double spaced, using Times New Roman font (size 12), with one-inch margins on all sides; citations and references must follow APA or school-specific format. Check with your professor for any additional instructions.

Include a cover page containing the title of the assignment, the studentâ€s name, the professorâ€s name, the course title, and the date. The cover page and the reference page are not included in the required assignment page length.
The specific course learning outcomes associated with this assignment are:

Examine the current ethical issues inherent throughout the criminal and civil justice systems.

Describe the dispensation of justice through the criminal and civil justice systems.

Use technology and information resources to research issues in the criminal court and the judicial process in America.

Write clearly and concisely about the American court system using proper writing mechanics and APA style conventions.
 

 

 
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Social Responsibility of Business” – Nursing Writers Hub

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Research, define and discuss social responsibility, what it means, and its role in business.
Your paper should be a minimum of 2 pages

 
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Assignment 3: Benefits of Business Analytics Business analytics can provide a significant benefit to organizations. If the organization utilizes business analytics…

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Assignment 3: Benefits of Business Analytics

Business analytics can provide a significant benefit to organizations. If the organization utilizes business analytics and analyzes the data correctly, they will be able to make informed decisions that will benefit the organization in many ways. They could use it to make decisions to address not only short-term company goals but also long-term strategic planning.

Using the Argosy University online library resources and the Internet, research two businesses within the same industry; one that utilizes business analytics and one that does not. Select at least 2 scholarly sources for use in this assignment.

Respond to the following questions:

  • Compare and contrast the two companies in terms of their use of business analytics to improve their position in the industry. You may select an organization you currently work for or one that you worked for in the past.
  • Provide your rationale as to whether or not the use of data analytics has helped the company accomplish its goals.
  • Describe the challenges the company may have faced by choosing to utilize business analytics that the other company did not face.

Make assumptions based on company history where required. Utilize at least 2 scholarly sources in support of your assertions.

Make sure you write in a clear, concise, and organized manner; demonstrate ethical scholarship in appropriate and accurate representation and attribution of sources; display accurate spelling, grammar, and punctuation.

Write a 3–4-page paper in Word format. Apply APA standards to citation of sources. Use the following file naming convention: LastnameFirstInitial_M1_A3.doc. For example, if your name is John Smith, your document will be named SmithJ_M1_A3.doc.

 

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The post Assignment 3: Benefits of Business Analytics Business analytics can provide a significant benefit to organizations. If the organization utilizes business analytics… appeared first on Nursing Writers Hub.