The Use of the Z-Test in Psychological Research

Directions for Z-Test DRAFT & FINAL Z-Test Writing Assignments Version 3

 

  1. You will turn in two versions of this paper:  the DRAFT version and FINAL version.
  2. You will turn in an electronic version of the DRAFT and FINAL version of your paper.
  3. Both the FINAL and DRAFT versions of the paper are worth 50 points, for a total of 100 points, or 10% of your grade.
  1. I will make edits to the draft version of your paper and return those edits to you in a timely manner.
  2. You will incorporate my written feedback into the final version of your paper.
  1. A LATE draft or final paper will result in an automatic 25-point deduction.
  2. Use the sub-headings and title that are given in the template below for your writing.  Do not alter the format or the text of the titles or sub-headings.  Do not remove the bolding from the headings.
  1. The purpose of this assignment is to get experience writing on a statistical topic, write according to an outline, and to describe the use of the Z-Test in psychological research.
  2. Consider your writing assignment as a take-home test. Do not work with any other student on the paper.
  3. Use double-spacing between lines (not 1.5-line spaces or fewer).
  1. Use 1-inch margins all around.
  2. Use 12-pt. font: Arial, Calibri, Helvetica, Verdana, Tahoma.  Do not use Times Roman—it is too hard to read.
  3. The DRAFT paper should be no shorter than 1,250 words.  The FINAL paper should be no shorter than 1,250 words.   Check the number of words in your writing.  Longer is not necessarily better.  Papers which are too long or too short will be downgraded.  Please see the rubric available for this assignment.
  4. Don’t quote and don’t copy (plagiarize) any material from any outside source.  You must write using your own words.  Quotes are extremely rare in psychological writing—DO NOT use QUOTES.
  5. Always save a copy of document for yourself as an attachment to an email (or somewhere).
  6. Do NOT use a right justified margin.  A right justified margin is one in which all the letters align on the right side.  Use a ragged right margin—in which the words do not align on the right side.  Here is more information about ragged right margin:

https://www.fonts.com/content/learning/fontology/level-2/making-type-choices/justified-vs-rag-right

  1. Include your name and class section (i.e. Section 20, 40, or 50).

 

Ask yourself whether you have:

  1. Corrected the grammar, spelling, punctuation
  2. Improved wording and deleted unnecessary words
  3. Do the sentences flow from one to the next?  Do not just answer questions.
  4. Reword to delete any quoted material
  5. Are all paragraphs indented?
  6. Is the material factually correct?
  7. Did you read through the paper to catch errors and improve readability?
  8. Does the paper sound as though it was written quickly and unfinished?

 

Here is the rubric, or scoring rules, for both your DRAFT and FINAL paper.  Each paper is worth 50 points for a total of 100 points across both papers.

 

Paper Rubric for DRAFT and FINAL Version

Criteria Ratings Pts
Accuracy & Content
Computations Correct
4 pts

Above Average

3 pts

Average

2 pts

Below Average

1 pt

Not Acceptable

4 pts
Description of concepts easy to understand
4 pts

Above Average

3 pts

Average

2 pts

Below Average

1 pt

Not Acceptable

4 pts
Covers all content requested
4 pts

Above Average

3 pts

Average

2 pts

Below Average

1 pt

Not Acceptable

4 pts
Defines statistical terms, includes formula(s)
4 pts

Above Average

3 pts

Average

2 pts

Below Average

1 pt

Not Acceptable

4 pts
Demonstrates mastery of material
4 pts

Above Average

3 pts

Average

2 pts

Below Average

1 pt

Not Acceptable

4 pts
Writing Ability  
No quoting or plagiarizing
4 pts

Above Average

3 pts

Average

2 pts

Below Average

1 pt

Not Acceptable

4 pts
Reread paper to correct easy to find mistakes
4 pts

Above Average

3 pts

Average

2 pts

Below Average

1 pt

Not Acceptable

4 pts
Generally well-written and easy to understand
4 pts

Above Average

3 pts

Average

2 pts

Below Average

1 pt

Not Acceptable

4 pts
Grammatically correct, such as the use of comma (,) semi-colon (;) and colon (:)
4 pts

Above Average

3 pts

Average

2 pts

Below Average

1 pt

Not Acceptable

4 pts
Spelling, correct word use, use whole sentences and not phrases (sentence includes a subject and a verb)
4 pts

Above Average

3 pts

Average

2 pts

Below Average

1 pt

Not Acceptable

4 pts
Formatting  
Use the headings, bolding provided and correct type of font, double-spaced, font size
2.5 pts

Above Average

1.5 pts Average 0.5 pts

Below Average

2.5 pts
Paper is not too long, not too short
2.5 pts

Above Average

1.5 pts Average 0.5 pts

Below Average

2.5 pts
Overall paper looks neat and orderly
2.5 pts

Above Average

1.5 pts Average 0.5 pts

Below Average

2.5 pts
Margins justified correctly
2.5 pts

Above Average

1.5 pts Average 0.5 pts

Below Average

2.5 pts
Total Points: 50 for the DRAFT paper

  

Total Points: 50 for the HARD COPY FINAL paper

 

A LATE draft or final paper will result in an automatic 25-point deduction.

 

 

 

Note:  Use the template on the next page as the format for your writing.  Delete all the text above this point.  Delete all the instructions from the template. 

 

 

The Use of the Z-Test in Psychological Research

Your Full Name, Section XX

Overview

            –DELETE THESE INSTRUCTIONS–In this section, give an overview of what you will talk about below.  [Hint: write the paper and then go back and summarize what you told us in 4-5 sentences using different words.  Make it interesting for the reader.]

What is the Z-Test?

            –DELETE THESE INSTRUCTIONS–When is the Z-Test used?  What descriptive statistics are being compared in the Z-Test?  What are the two Z-Test formulas?  Define each of the statistical terms used in the Z-Test formulas.  What important statistical distribution is the observed Z-Test compared to—i.e., what is the name of that distribution?  What does “the Z-Test is significant” mean—is that a good thing or a bad thing? If the result is significant, what can be said about the difference between the means?  What is the probability value (i.e., the numbered value) that is associated with the small probability cut off?  Out of 100 chances how many chances is the small probability cut off (for example 10 chances out of 100 is a probability of .10)?  When you calculate the Z-Test is the result expressed as a Z-Score?

Application of the Z-Test

–DELETE THESE INSTRUCTIONS FROM HERE–Below are four research studies in which a Z-Test is used to analyze the data.  Except for screenshots, you will use full sentences to describe the results.

Here are the sections you will use for each problem.

  1. Research Question and Independent and Dependent Variables

State the research question.  Indicate what the independent variable is and what the dependent variable is.

  1. Assign Numbers to the Correct Statistical Terms (Mu, Sigma, SD, n, and X-Bar)

Assign each number to the correct statistical terms.  You will use these statistical terms:  Mu, Sigma, SD, n, and X-Bar.   Remember to use full sentences.

  1. Screenshot or Drawing of Formula Used and Numbers Assigned to the Formula

Write the formula for the Z-Test that you are using.  This can be done by drawing within your document or a screenshot of another document.

Remember, there are two versions of the Z-Test formula.  You use the one that is applicable to your specific problem.

You will use graphics (such as a screen capture) to write the formula you used and the numbers in the formula.  For each problem, your screenshot or drawing will include the formula that contains the numbers from the problem.  For example, this is showing the work for the problem used in class about stress and college athletes:

 

 

 

  1. Observed Value of the Test Statistic

Specifically state the value of the observed value of the test statistic in a sentence.  Only one sentence is needed.

  1. Small or Not Small Probability and Why

Find the observed probability for your observed value. State what the observed probability is and whether it is small or not small.  Why is the probability small or not small?

  1. Significant or Not Significant and Why

Determine whether the result is significant or not significant.  Why do you conclude that?

  1. Conclusion

Tell what the result of the study is in terms of the effect of the independent on the dependent variable.  Explain why you come to that conclusion.  –DELETE TO HERE —

Problem 1:   SAT Prep Program

A sample of 25 high school students complete a preparation program for taking the SAT test.  Here are the SAT scores from the 25 students who completed the SAT prep program:

434 694 457 534 720 400 484 478 610 641 425 636 454

514 563 370 499 640 501 625 612 471 598 509 531

The population average for SAT scores is 500 with a standard deviation of 100.  Did the students who took the SAT-prep course get a significantly higher SAT score than the general population to SAT test takers?

  1. Research Question and Independent and Dependent Variables
  2. Assign Numbers to the Correct Statistical Terms (Mu, Sigma, SD, n, and X-Bar)
  3. Screenshot or Drawing of Formula Used and Numbers Assigned to the Formula
  4. Observed Value of the Test Statistic
  5. Small or Not Small Probability and Why
  6. Significant or Not Significant and Why

 

  1. Conclusion and Why

 

Problem 2:   Parking Space Wars

A CSUSM student wondered about the differences in time to find a parking spot across the universities in San Diego.  The average time to find a parking space at all San Diego universities is 30 minutes.  A sample of 16 CSUSM students took an average of 25 minutes to find a parking spot at CSUSM with a standard deviation of 8.

  1. Research Question and Independent and Dependent Variables
  2. Assign Numbers to the Correct Statistical Terms (Mu, Sigma, SD, n, and X-Bar)
  3. Screenshot or Drawing of Formula Used and Numbers Assigned to the Formula
  4. Observed Value of the Test Statistic
  5. Small or Not Small Probability and Why
  6. Significant or Not Significant and Why

 

  1. Conclusion

 

Problem 3:  Covid Symptoms Predictor

A researcher wanted to compare the effectiveness of a new CT imagery technique for diagnosing Covid to standard laboratory method.  The population of standard Covid laboratory method yielded an average accuracy score of 80% with a standard deviation of 10.  In a sample of 16 patients using a new CT imagery technique, the average accuracy score was 84%.

  1. Research Question and Independent and Dependent Variables
  2. Assign Numbers to the Correct Statistical Terms (Mu, Sigma, SD, n, and X-Bar)
  3. Screenshot or Drawing of Formula Used and Numbers Assigned to the Formula
  4. Observed Value of the Test Statistic
  5. Small or Not Small Probability and Why
  6. Significant or Not Significant and Why

 

  1. Conclusion

 

Problem 4:  Dating App Comparison

The developers of a new dating app for college students wondered how it fared against the most popular app in the U.S.  Research indicates that Tinder is the most popular dating app among college students with an average favorability rating of 85%.  A new dating app called Binge was product-tested at CSUSM.  Twenty-five students participated in the product testing and their average rating of Binge was 81.5% with a standard deviation of 10.

  1. Research Question and Independent and Dependent Variables
  2. Assign Numbers to the Correct Statistical Terms (Mu, Sigma, SD, n, and X-Bar)
  3. Screenshot or Drawing of Formula Used and Numbers Assigned to the Formula
  4. Observed Value of the Test Statistic
  5. Small or Not Small Probability and Why
  6. Significant or Not Significant and Why

 

  1. Conclusion

Summary

 

–DELETE THESE INSTRUCTIONS–Briefly restate what you have stated based on all of the paper written above but use different words.  What did you learn from this assignment or what could someone learn from reading your paper?