MATH 225N Week 6 Discussion: Confidence Intervals
Chamberlain University MATH 225N Week 6 Discussion: Confidence Intervals– Step-By-Step Guide
This guide will demonstrate how to complete the Chamberlain University MATH 225N Week 6 Discussion: Confidence Intervals 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 MATH 225N Week 6 Discussion: Confidence Intervals
Whether one passes or fails an academic assignment such as the Chamberlain University MATH 225N Week 6 Discussion: Confidence Intervals 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 MATH 225N Week 6 Discussion: Confidence Intervals
The introduction for the Chamberlain University MATH 225N Week 6 Discussion: Confidence Intervals 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.
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How to Write the Body for MATH 225N Week 6 Discussion: Confidence Intervals
After the introduction, move into the main part of the MATH 225N Week 6 Discussion: Confidence Intervals 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 MATH 225N Week 6 Discussion: Confidence Intervals
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 MATH 225N Week 6 Discussion: Confidence Intervals
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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Sample Answer for MATH 225N Week 6 Discussion: Confidence Intervals
I took a data set of n = 35 values for Height measured in Inches and I used our Week 6 Excel spread sheet Calculator ( please see Week 6 Files area after first clicking Files along the left of the computer screen ) and I calculated 4 confidence intervals with the same sample mean and same sample size and same population standard deviation.
The 4 confidence levels were ( respectively ) 99% 95% 90% 85%
Notice that the 4 margins of error were ( respectively ) 1.57 inches 1.19 inches 1.00 inches 0.88 inches
If this is not a coincidence – that is – if this trend / pattern holds up in general ( at least for the confidence intervals for one population mean that we study and learn about in this course ) then how would you put that pattern / trend into words ??
In other words, all other things being equal ( the same or “fixed” ) , what happens to the margin of error when the confidence level is increased ?? ( or decreased ?? )
Thanks Friends and please see attached ( see the tab along the bottom for the z confidence interval – sample size larger than 30 – the left most tab along the bottom of the spread sheet ) 😉
The original height data used are attached to the next Post
That is where the sample mean and population standard deviation came from.
I used population standard deviation rather than sample standard deviation because the sample size of n = 35 was larger than 30
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Sample Answer 2 for MATH 225N Week 6 Discussion: Confidence Intervals
I tried another experiment with confidence intervals.
I calculated 4 95% confidence intervals all using the same sample mean of 65.8857 inches and the same population standard deviation of 3.5998 inches.
The only difference between the 4 95% confidence intervals is that I based the calculations of the confidence interval endpoints ( left endpoint and right endpoint ) on 4 different sample sizes of n = 35 and then n = 70 and then n = 105 and then n = 140 .
The 4 ( respective ) margins of error were 1.19 inches 0.84 inches 0.69 inches 0.60 inches
If this is not a coincidence – if the confidence interval for one population mean that we study and learn about in this course always behaves according to this trend / pattern – how can you put this trend / pattern into words ??
That is, all other things being equal ( the same or “fixed” ) then what happens to the margin of error as the sample size is increased ??
Another way of thinking about this is – if you use a larger sample size you are incorporating “more information” into the analysis – so what is the “reward” for doing that in this case ??
😉
The n = 35 spread sheet is attached to this Post and the spread sheets for ( respectively ) n = 70 and then n = 105 and then n = 140 are attached to 3 further Posts just below here.
Thanks Friends and please see attached ( see the tab along the bottom for the z confidence interval – sample size larger than 30 – the left most tab along the bottom of the spread sheet ) 😉
Be sure to focus on just the 95% confidence interval and its margin of error in each of the 4 spread sheets
Thanks Friends and Very Best Wishes and Good Luck during this Week 6 !!
This Week is a busy one because we have to complete the Week 6 Knewton Quiz and also get off to a great start on the Week 7 lab turn in assignment in the SAME Week !!
Good Luck and THANK YOU so much for your hard work !!
Sample Answer 3 for MATH 225N Week 6 Discussion: Confidence Intervals
One of the things I track is door to electrocardiogram time (D2EKGT) and door to balloon time (D2BT) for ST elevation myocardial infarction (STEMI) patients. EKG, taken from the German spelling, is often used because ECG can be confused with echocardiograms. Studies have shown that getting the EKG is done in 10 minutes or less translates to quicker reperfusion times. One such study was done in the National Taiwan University Hospital in 2014 (Lee et al., 2019) and showed that the D2EKGT was the most critical interval of delay in getting patients to the cath lab and reperfused. Therefore, it is something my department keeps a watchful eye on with every STEMI.
In that study, they created an EKG station in the triage area so they wouldn’t have to transport the patients to another area to do an EKG. Patients who arrived after the new EKG station was created were the intervention group, and their D2EKG and D2B times were compared to a somewhat equal number of patients that came to the emergency department in the months before the EKG station was put in the triage area; those were the control group (Lee et al., 2019). The required sample size was 62 patients in each group (intervention and control) with 80% power and a type 1 error of 0.05 (Lee et al., 2019). This isn’t covered until Chapter 9 in our text, and since I found Chapter 8 confounding enough, I will worry about what that means later. However, the following is something easy to understand. One example in the study compared the D2EGKT of walk-in patients and how it affected the D2BT before and after the change in the triage area (Lee et al., 2019): 93.3% of walk-in patients got their EKGs in <10 mins after the change vs 79.8% before the EKG station was set up in the triage area. This translated to 91.1% of those patients having a D2BT <90 mins vs 76.2% before (Lee et al., 2019).
If I wanted to reproduce that in my hospital, I think I’d have to apply the confidence interval for the population mean. As per this week’s online lesson (Chamberlain University, 2021), interpreting confidence interval is based on repeated sampling. A 95% confidence interval means that if I had 100 different samples each with a different mean, 95 would contain the population value and 5 would not. I hope my understanding is correct that they mean sets of 100 values, so you can get varying means. For the 93.3% of walk-in patients who got their EKG in <10 minutes in the Taiwan study, to replicate that with 95% confidence interval, and assuming 100 patients, the calculated lower limit would be 89 patients and the upper limit would be 98 patients. The excel calculations show fractions, but as per our lesson, we cannot go below a minimum and we cannot sample a fraction of a person, so we round up, not down (Chamberlain University, 2021).
Lowering the confidence interval to 90% changes the lower and upper limits to 90 and 97 respectively. Raising the confidence interval to 99% changes the lower and upper limits to 87 and 99. The CI of 90% gives us a narrower interval range but we’d rather have the higher confidence of 95%, right? That is the “trade off” described on page 340 of our text and demonstrated by the curve Figure 8.6 (Holmes et al., 2018). Increasing the CI to 99% makes the interval even wider.
So, if my understanding is correct, and I wanted to replicate the success seen in Taiwan with 95% confidence, I’d need 89 to 98 patients of 100 to get their D2EKG times to <10 minutes. Is that correct?
Thanks,
Elaine
Chamberlain University. (2021). MATH225. Week 6: Confidence intervals (Online lesson). Downers Grove, IL: Adtalem.
Holmes, A., Illowsky, B., & Dean, S. (2018). Introductory business statistics. OpenStax.
Lee, C., Meng, S., Lee, M., Chen, H., Wang, C., Wang, H., Liao, M., Hsieh, M., Huang, Y., Huang, E., Wu, C. (2019). The impact of door-to-electrocardiogram time on door-to-balloon time after achieving the guideline-recommended target rate. PLoS ONE 14 (9), 1-14. https://chamberlainuniversity.idm.oclc.org/login?url=https://search.ebscohost.com/login.aspx?direct=true&db=a9h&AN=138516728&site=eds-live&scope=siteLinks to an external site.
Sample Answer 4 for MATH 225N Week 6 Discussion: Confidence Intervals
MY TAKE ON t DISTRIBUTIONS
t Distributions are reflected on page 7 of 8 of our ( attached ) 8 page formula and table document for the course.
t Distributions come up in Weeks 6-7 of our course when we are working on the “mean case” AND if the population standard deviation is not known / not given.
One of the aspects of t Distributions that is new for you is the concept of degrees of freedom.
In Weeks 6-7 of our course, the formula for degrees of freedom is df = n – 1
Like the normal distributions, the t Distributions are symmetrical / bell shaped.
But t Distributions are different from normal distributions, and one of the ways that you should hopefully see and realize that is that normal distributions ( the standard normal distribution ) is reflected on page 6 of 8 of our attached document here while t Distributions are reflected on page 7 of 8 of our attached document here.
Thanks Friends and please see the slides below for some more background about t Distributions that will help you during Weeks 6-7 of the course.
Thanks and Best Wishes !!
Sample Answer 5 for MATH 225N Week 6 Discussion: Confidence Intervals
This gets me too. What I have read is they seem to be the same, but what I took from everything I looked up, and that was multiple sights, is that the standard deviation and the margin of error work together? Not sure if that is right, but it is what I took from my research of the two. Per Glen (2020). “The margin of error is the range of values below and above the sample statistic in a confidence interval. The confidence interval is a way to show what the uncertainty is with a certain statistic (i.e. from a poll or survey). With Standard Deviation, you must know the population parameters to calculate it. The margin of error can be calculated in two ways, depending on whether you have parameters from a population or statistics from a sample: Margin of error = Critical value x Standard deviation for the population. Margin of error = Critical value x Standard error of the sample” (p. 1).
Reference:
Glen, S. (2020). “Margin of Error: Definition, How to Calculate in Easy Steps” From StatisticsHowTo.com.Links to an external site. Elementary Statistics for the rest of us! https://www.statisticshowto.com/probability-and-statistics/hypothesis-testing/margin-of-error/Links to an external site.