MATH 225N Discussion Hypothesis Testing

MATH 225N Discussion Hypothesis Testing

MATH 225N Discussion Hypothesis Testing

Our Week 7 initial prompt / cue is a little more open ended and vague than perhaps what might be usual so I wanted to provide you with something to help guide you a little bit.  I won’t share the raw concrete data with you or any of the Excel spread sheets that I used until later in the Week 7.  Notice that the assignment does not necessarily require you to provide data or to go through all of the finer and more technical details of all of this ( a full blown hypothesis testing example ) but that notwithstanding, the more thought you put into this assignment and the more details that you provide, the better.  Please note my follow up Post to this Post where I give some details about where the calculated z value ( the calculated value for the test statistic ) would come from if an Excel spread sheet had not been used to get it.  Thanks Friends and Best Wishes and Good Luck !!

Describe a hypothesis test study that would help your work or conclusions in some way. Describe what variable would be tested and what would be your guess of the value of that variable. Then include how the result, if the null were rejected or not, might change your conclusions or actions in some way.

My research question is: using the May 2009 data set, determine if there is sufficient evidence to conclude that the average amount of births is less than 5000 in the United States and territories, at the alpha significance level of 0.01

We will use the appropriate data and the appropriate spread sheet and the appropriate sheet within the correct spread sheet to calculate the calculated value for the test statistic and to calculate the P-value.

If the P-value is greater than the alpha significance level, the decision would be Do Not Reject the Null Hypothesis

If the P-value is smaller than the alpha significance level, the decision would be Reject the Null Hypothesis

I am using the alpha significance level of 0.01

So for me here        

Based on my research question above, my hypotheses are:

( Pretend that there is a colon with two dots in each of those instead of the three dots !!  I could not seem to get a colon to go in there !! )

From the Excel spread sheet provided elsewhere ( attached to another Post ) ( the hypothesis testing calculator spread sheet ) , using the 52 values for births from my May 2009 data set, the sample mean was

and the population standard deviation was

and the alpha significance level was as above and the hypothesized value from the null hypothesis was 5000 and the sample size of course was        

The output included a calculated value for the test statistic of

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and a P-value of

and based on    P-value  >  alpha significance level

that is        0.9436  >  0.01

the decision of course was Do Not Reject the null hypothesis

which is Do Not Reject    

The interpretation and conclusion therefore is as follows:

At the 

significance level and for these particular collected and analyzed sample data, there is NOT sufficient sample evidence to conclude that the average amount of births is less than 5000 in the United States and territories.

The reasons I would analyze the Births, Deaths, Marriages, Divorces data for the 50 States and other areas such as Washington DC and Puerto Rico and other similar places ( such as perhaps Guam / US Virgin Islands ) is to get a feel for how much healthcare capacity is needed for delivering babies and for caring for the family from before conception to long after the actual birth.  Also, noting Deaths data and trends also foreshadows the need for healthcare capacity in that we might surmise if the overall population is perhaps getting older on average or sicker on average or what not – again foreshadowing the healthcare capacity that we might need to build and maintain.  Keeping track of Marriages data also foreshadows the need for healthcare capacity as increases in Marriages for example might also foreshadow more subsequent births and the need for more healthcare capacity to accommodate that.

MATH 225N Discussion Hypothesis Testing
MATH 225N Discussion Hypothesis Testing

Thanks Friends and take good care and best wishes too !!

It looks like you might have had some trouble trying to get a graphic / image into your Post and so I wanted to try it out for myself and see if I could get it to work. 😉

The process involved a couple of unexpected steps for me, so I will share as much as I can here to hopefully help Folks who might want to place something like this in a Post during Weeks X-X . 😉

XXXXX gave some great instructions on doing this kind of thing too, but I have a variation on a few of the steps that she performed. 😉

First, before copying and pasting the Excel output to an open blank Word document, I had to go through the very irritating step of giving all the cells to be copied and pasted a sort of light background – that orangy peachy color that you see.

Otherwise when I created my jpg / jpeg most of the cells were dark black and not readable so to speak.

Next in Excel I highlighted the cells to be copied and then did contol c

Then in a blank Word document I used the mouse and clicked but had to be careful about which Paste option that I used – I had to use Paste as a picture, which was one of the last options available to me from left to right.

Then I clicked on the image in the Word document and did Save as Picture

Then I saved it to my desktop and saved it as a jpg / jpeg

Then in the course shell I clicked on Files and then clicked on Week X Files

Then I uploaded my newly created image from my desk top into the Week X Files area

Then in my Post I clicked on Embed Image and then clicked CANVAS and then clicked Course Files and then clicked Week X Files

Then I located my desired image and clicked on it

Then I scrolled down a bit and clicked Update or whatever it is…

Then the image magically appeared in this Post ! 🙂

So the two steps that surprised me the most were having to give all the cells a light background and secondly instead of just blindly pasting into Word I had to be thoughtful and intentional about “which” “paste method / type” to use.

Thanks XXXXX and Best Wishes and please enjoy the upcoming Week X and work hard and learn a lot !

I really appreciate that very much !!

I wanted to give you some details about where the calculated z value and the P-value for the above Hypothesis Testing example would come from if we had not used Excel spread sheets to find those things.

In this context and setting and circumstance, the calculated value for the z test statistic comes from:

so that here we get

Now using the attached Table ( page 6 of pdf ) we estimate the P-value to be

P( z < 1.586 )    

P( z < 1.59 )    =    0.9441

We get an answer here slightly different from the approximate P-value from an Excel spread sheet because the Excel spread sheet literally used z = 1.586 to calculate the approximate P-Value of 0.9436 .


Notice ( using the Table attached ) that          0.9429  <  P-Value = 0.9436  <  0.9441


1.58  <  z = 1.586  <  1.59


Thanks Friends and Best Wishes !!

Later in the Week 7 I will share the actual raw concrete data with you as well as the Excel spread sheets which were used to calculate the calculated value for the test statistic and the P-value here.

Note that this was an example of a lower tail ( left tail ) test with population standard deviation known and sample size larger than n = 30 ( since n = 52 for this example ) .

Enjoy Friends !!


PS      Friends most of what you see in this Post here – you would never “do things that way” during Week 7 of the course – we use Excel spread sheet calculators to the MAXIMUM POSSIBLE EXTENT while working on problems and exercises in the course – these details in this Post here are just provided for your edification and to reveal some of the things that Excel spread sheet calculators “are doing” to give us output areas and answers during Week 7 of our course here.  Thanks Friends and Good Luck !!

I’d like to investigate follow-up after discharge for COVID-19 patients and how that relates to any subsequent hospitalization later for cardiovascular issues. We know that COVID-19 makes people hypercoagulable which increases risk of complications and even after recovery (Ciaburri, 2020), and some COVID-19 patients return to the hospital with cardiovascular complications (Rastogi and Twarei, 2020). I would hypothesize that patients who follow up with their doctors for venous thromboembolism (VTE) prophylaxis post discharge have better 6-month hospital readmission rates for cardio-vascular event compared to patients who do not follow up.  Readmission in 6 months is my variable X, and this is a population proportion test.
My hypothesis could be a two-tailed test with one being no admissions in 6 months and the other being any admission in 6 months. As per our lesson, I’d write the claim first, which may be the null or the alternative hypothesis, and then write the complement to the claim (Chamberlain University, 2021). My null hypothesis for patients who comply with follow up is no cardio-vascular related readmissions, or Ho p = 0, and the alternative would be Ha p ≠ 0. 
I hypothesize that receiving proper care in the recovery phase of COVID-19 will prove beneficial in preventing readmissions. If the numbers prove me wrong, then I must reject my null hypothesis, and “assume there is enough evidence to support the alternative hypothesis” (Holmes et al., 2018, p. 403). 
As per the Chamberlain University on-line lesson, failure to reject the null hypothesis does not mean we have to accept the alternative hypothesis (2021). So, does that also mean that rejecting the null does not mean we accept the alternative hypothesis, or simply that we need more data? According to Ciaburri (2020), almost a third of COVID-19 patients experienced thrombotic complications, but age was also an independent risk factor.  That information may cause me to rethink my hypothesis, but as a nurse, I would still urge patient education upon discharge that includes following up with the doctor as an outpatient.
Chamberlain University. (2021). MATH225. Week 7: hypothesis testing [Online lesson]. Downers Grove, IL: Adtalem.
Ciaburri, J. (2020). Hypercoagulability in COVID-19 patients. International student journal of nurse anesthesia, 19(2), 23-30.
Holmes, A., Illowsky, B., & Dean, S. (2018). Introductory business statistics. Openstax.
Rastogi, A., Twarei, P. (2020). Covid 19 and its cardiovascular effects. Annals  of cardiac anaesthesia, 23(2),401-408.