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NUR 705 Assignment 7.1: Z-Scores

NUR 705 Assignment 7.1: Z-Scores

ST. Thomas University NUR 705 Assignment 7.1: Z-Scores-Step-By-Step Guide

This guide will demonstrate how to complete the ST. Thomas University NUR 705 Assignment 7.1: Z-Scores  assignment based on general principles of academic writing. Here, we will show you the A, B, Cs of completing an academic paper, irrespective of the instructions. After guiding you through what to do, the guide will leave one or two sample essays at the end to highlight the various sections discussed below.

How to Research and Prepare for NUR 705 Assignment 7.1: Z-Scores                                                      

Whether one passes or fails an academic assignment such as the ST. Thomas University NUR 705 Assignment 7.1: Z-Scores   depends on the preparation done beforehand. The first thing to do once you receive an assignment is to quickly skim through the requirements. Once that is done, start going through the instructions one by one to clearly understand what the instructor wants. The most important thing here is to understand the required format—whether it is APA, MLA, Chicago, etc.

 

After understanding the requirements of the paper, the next phase is to gather relevant materials. The first place to start the research process is the weekly resources. Go through the resources provided in the instructions to determine which ones fit the assignment. After reviewing the provided resources, use the university library to search for additional resources. After gathering sufficient and necessary resources, you are now ready to start drafting your paper.

How to Write the Introduction for NUR 705 Assignment 7.1: Z-Scores                                                    

The introduction for the ST. Thomas University NUR 705 Assignment 7.1: Z-Scores   is where you tell the instructor what your paper will encompass. In three to four statements, highlight the important points that will form the basis of your paper. Here, you can include statistics to show the importance of the topic you will be discussing. At the end of the introduction, write a clear purpose statement outlining what exactly will be contained in the paper. This statement will start with “The purpose of this paper…” and then proceed to outline the various sections of the instructions.

How to Write the Body for NUR 705 Assignment 7.1: Z-Scores                                                    

After the introduction, move into the main part of the NUR 705 Assignment 7.1: Z-Scores   assignment, which is the body. Given that the paper you will be writing is not experimental, the way you organize the headings and subheadings of your paper is critically important. In some cases, you might have to use more subheadings to properly organize the assignment. The organization will depend on the rubric provided. Carefully examine the rubric, as it will contain all the detailed requirements of the assignment. Sometimes, the rubric will have information that the normal instructions lack.

 

Another important factor to consider at this point is how to do citations. In-text citations are fundamental as they support the arguments and points you make in the paper. At this point, the resources gathered at the beginning will come in handy. Integrating the ideas of the authors with your own will ensure that you produce a comprehensive paper. Also, follow the given citation format. In most cases, APA 7 is the preferred format for nursing assignments.

How to Write the Conclusion for NUR 705 Assignment 7.1: Z-Scores                                                    

After completing the main sections, write the conclusion of your paper. The conclusion is a summary of the main points you made in your paper. However, you need to rewrite the points and not simply copy and paste them. By restating the points from each subheading, you will provide a nuanced overview of the assignment to the reader.

How to Format the References List for NUR 705 Assignment 7.1: Z-Scores                                                      

The very last part of your paper involves listing the sources used in your paper. These sources should be listed in alphabetical order and double-spaced. Additionally, use a hanging indent for each source that appears in this list. Lastly, only the sources cited within the body of the paper should appear here.

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NUR 705 Assignment 7.1: Z-Scores

Assignment Guidelines

Complete the problems on Z-scores (Word)Links to an external site.. Please complete your work manually and upload a picture to the assignment tab. You must show your work for full credit.

Submission

Submit your assignment on the Assignment 7.1: Z-Scores page.

Week 7: Statistical Significance

Lesson 1: Statistical Significance

Introduction

In this week, you will explore foundational principles of inferential statistics.

In Week 4, you learned about hypothesis testing. This week, you will examine whether or not an observed difference can be attributed to chance, or whether it can be associated with a variable.

Learning Outcomes

At the end of this lesson, you will be able to:

  • Understand how correctly developing a null hypothesis contributes to interpretation of statistical tests
  • Understand the relationship between standard normal distribution and probability
  • Navigate the z-score table.
  • Interpret a confidence interval
  • Understand the principles behind level of significance

Before attempting to complete your learning activities for this week, review the following learning materials:

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Learning Materials

Read the following in your Kim, Mallory, & Vallerio (2022) Statistics for evidence-based practice in nursing textbook:

NUR 705 Assignment 7.1 Z-Scores
NUR 705 Assignment 7.1 Z-Scores

Chapter 6, page 109, starting at “Normal Distribution” and ending at page 122

Read the following in your Polit & Beck (2021) Nursing research: Generating and assessing evidence for nursing practice textbook:

  • Chapter 3, page 57, starting at the “Results” section and ending at “The Discussion” section
  • Chapter 18, page 388, starting at “Hypothesis Testing” and ending at page 391 at “One-Tailed and Two-Tailed Tests”
  • Chapter 21, page 454, starting at “Precision of Results” and ending at page 457 at “Interpreting Mixed Results”

The Empirical Rule

Review the video on using the empirical rule:

Empirical Rule TranscriptLinks to an external site.


Against All Odds: Tests of Significance

View the presentation by Dr. Pardis Sabeti to learn about tests of significance.

Sabeti, P. (Host), & Villiger, M. (Writer/Producer/Director). (2014). Tests of significanceLinks to an external site. [Video Unit 25]. Against all Odds: Inside statistics. Retrieved from Annenberg LearnerLinks to an external site.. (Transcript is provided on the video page.)


Lecture: Significance Testing, Part 1

Review the lecture to learn more about tests of significance.

Significance Testing, Part 1 TranscriptLinks to an external site.


Z-Scores

Review the video on Z-Scores, standardization, and the standard normal distribution:

Z-Scores and Standardization TranscriptLinks to an external site.

Lecture: Calculating Z-Scores

Review the lecture to learn more about calculating z-scores.

Z-Scores Lecture TranscriptLinks to an external site.


Normal Distribution Problems: Z-Score

Review the video on normal distribution problems: z-score:

Normal Distribution Problems: Z-Score TranscriptLinks to an external site.


Against All Odds: Confidence Intervals

View the presentation by Dr. Pardis Sabeti to learn more about how a sample size affects the margin of error.

Sabeti, P. (Host), & Villiger, M. (Writer/Producer/Director). (2014). Confidence intervalsLinks to an external site. [Video Unit 24]. Against all odds: Inside statistics. Retrieved from Annenberg LearnerLinks to an external site.. (Closed captioning is provided.)

Confidence Intervals TranscriptLinks to an external site.

Z-Scores and Standardization Transcript

In this video, we’ll be learning about Z scores and standardization. By learning about both of these topics, you will learn how to calculate exact proportions using the standard normal distribution.

What is the standard normal distribution? The standard normal distribution is a special type of normal distribution that has a mean of zero and a standard deviation of one. Because of this, the standard normal distribution is always centered at zero, and has intervals that increase by one. Each number on the horizontal access corresponds to Z score. A Z score tells us how many standard deviations an observation is from the mean mu. For example, a Z score of -2, tells me that I am two standard deviations to the left of the mean, and Z score of 1.5 tells me that I am one and a half standard deviations to the right of the mean.

Most importantly, a Z score allows us to calculate how much area that specific Z score is associated with. And we can find what that exact area using something called Z score table, also known as the standard normal table. This table tells us the total amount of area contained to the left side of any value of Z. For this table, the top row, and the first column correspond to Z values, and all the numbers in the middle correspond to areas.

For example, according to the table, a Z score of -1.95 has an area of 0.0256 to the left of it. To save this in a more formal manner. We can say that the proportion of Z less than -1.95 is equal to 0.0256. We can also use the standard normal table to determine the area to the right of any Z value. All we have to do is take one minus the area that corresponds to the Z value.

For example, to determine the area to the right of Z score of 0.57, all we have to do is find the area that corresponds to this Z value, and then subtract it from one. According to the table, the Z score of 0.57 has an area of 0.7157 to the left of it. So 1-0.7157 gives us an area of 0.2843. And that is our answer.

The reason why we can do this is because we have to remember that the normal distribution is a density curve, and it always has a total area equal to one or 100%. You can also use the Z score table to do a reverse lookup, which means you can use the table to see what Z score is associated with a specific area. So if I wanted to know what value of Z corresponds to an area of 0.8461 to the left of it, all we have to do is find 0.8461 on the table, and see what value of Z it corresponds to. We see that it corresponds to a Z value of 1.02. The special thing about the standard normal distribution is that any type of normal distribution can be transformed into it. In other words, any normal distribution with any value of Mu and Sigma can be transformed into the standard normal distribution, where you have a Mu of zero and a standard deviation of one.

This conversion process is called standardization. The benefit of standardization is that it allows us to use the Z score table to calculate exact areas for any given normally distributed population with any value of Mu or Sigma. Standardization involves using this formula. This formula says that the Z score is equal to an observation X minus the population mean Mu, divided by the population of standard deviation Sigma.

So suppose that we gathered data from last year’s final chemistry exam and found that it followed a normal distribution with a mean of 60 and a standard deviation of 10. If we were to draw this normal distribution, we would have 60 located at the center of the distribution, because it is the value of the mean. And each interval would increase by 10, since that is the value of the standard deviation. To convert this distribution, to the standard normal distribution, we will use the formula.

The value of Mu is equal to 60, and the value of Sigma is equal to 10. We can then take each value of X and plug it into the equation. If I plug in 60, I will get a value of zero. If plug in 50, I will get a value of -1. If I plug in 40, I will get a value of -2. If we do this for each value, you can see that we end up with the same values as a standard normal distribution.

When doing this conversion process, the mean of the normal distribution will always be converted to zero. And the standard deviation will always correspond to a value of one. It’s important to remember that this will happen with any normal distribution, no matter what value the Mu and Sigma are. Now, if I asked you what proportion of students score less than 49 on the exam, it is this area that we are interested in. However, the proportion of X less than 49 is unknown until we use the standardization formula.

After plugging in 49 into this formula, we end up with a value of -1.1. As a result, we will be looking for the proportion of Z less than -1.1. And finally, we can use the Z score table to determine how much area is associated with the Z score. According to the table, there’s an area of 0.1357 to the left of this Z value. This means the proportion of Z less than -1.1 is 0.1357. This value is in fact, the same proportion of individuals that scored less than 49 on the exam. As a result, This is the answer.

Let’s do one more example. When measuring the heights of all students at a local university, it was found that it was normally distributed with a mean height to 5.5 feet and a standard deviation of 0.5 feet. What proportion of students are between 5.81 feet and 6.3 feet tall? Before we solve this question, it’s always a good habit to first write down important information. So we have a Mu of 5.5 feet and a Sigma of 0.5 feet. We are also looking for the proportion of individuals between 5.81 feet and 6.3 feet tall. This corresponds to this highlighted area.

To determine this area, we need to standardize the distribution. So we will use the standardization formula. Plugging in 5.81 to this formula gives us a Z score of 0.62 and plugging in 6.3 into the formula, gives us a Z score of 1.6. According to the standard normal table, the Z score of 0.62 corresponds to an area of 0.7324, and the Z score of 1.6 corresponds to an area of 0.9452. To find the proportion of values between 0.62 and 1.6, we must subtract the smaller area from the bigger area. So 0.9452 minus 0.7324 gives us 0.2128. As a result, the proportion of students between 5.81 feet and 6.3 feet tall is 0.2128.

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