## MATH 225N Week 6 Discussion: Confidence Intervals

MATH 225N Week 6 Discussion: Confidence Intervals

For grading purposes, this particular discussion posting area runs from Sunday Feb 7 through Sunday Feb 14, inclusively. We explore inferential statistics this Week. This includes estimation ( confidence intervals ), a confidence interval for a mean, and a confidence interval for a proportion. We explore concepts such as the concept of a point estimate and the concept of a margin of error for a confidence interval. We explore concepts such as “confidence level” as well. Please don’t forget to use an “outside” resource as part of the content and documentation for your first Post – the Post which is due on or before Wednesday of the Week – the Post where you make the most major contribution to the Weekly discussion posting area and attempt to address the discussion prompts / cues for the Week. It could possibly include a web site that you discovered on the internet at large, so long as the web site is relevant and substantial and does not violate the Chamberlain University policy for prohibited web sites, and so forth. It could possibly include references / resources that you discover through making use of the online Chamberlain University Library ( please click Resources along the left and then click Library to discover the link to the Chamberlain University online Library ) .

Check out the link below for some information about confidence intervals, the so-called margin of error, critical value( s ), and when to use t Distributions rather than normal distributions when finding a confidence interval under certain circumstances. Link (Links to an external site.)Links to an external site. This is one kind of an example of using an “outside” source / resource to add to what is revealed in our Weekly Lesson in Modules and in our Weekly text book reading. Please don’t forget to look over the Graded Discussion Posting Rubric each Week to be certain that you are meeting all of the Frequency requirements as well as all of the Quality requirements for graded discussion posting each Week. If you have any questions about anything, please do not hesitate to post in the Q & A Forum discussion posting area or to send me a direct e-mail message to CSmith10@chamberlain.edu Thanks Friends and Good Luck ! Work hard and learn a lot !! Sincerely, Mr. Smith Chamberlain University Math, Statistics, and Quantitative Research CSmith10@chamberlain.edu

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

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,

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.