Week 7 Discussion: Hypothesis Testing

For grading purposes, this particular discussion posting area runs from Sunday Feb 14 through Sunday Feb 21, inclusively.

We explore inferential statistics this Week. This includes significance testing ( hypothesis testing ) . We study a hypothesis test for a mean and separately a hypothesis test for a proportion. We study concepts such as null hypothesis, alternative hypothesis, test statistic, significance level, p value, type I error, type II error, and statistical “power.”

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 a discussion about so-called “statistical power.”  Statistical power is related to Type II Errors and beta.  We also learn about Type I Errors, alpha, and significance level in Week 7 .

Hi Friends and Greetings !!

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        �=0.01

Based on my research question above, my hypotheses are:

�0⋮�≥5000

��⋮�<5000

( 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

�≈6695

and the population standard deviation was

�≈7707.933

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        �=52

The output included a calculated value for the test statistic of

�≈1.586

and a P-value of

�−�����≈0.9436

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    �0

The interpretation and conclusion therefore is as follows:

At the �=0.01

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.

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

Hello Professor and classmates:
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.
Elaine
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. https://chamberlainuniversity.idm.oclc.org/login?url=https://search.ebscohost.com/login.aspx?direct=true&db=c8h&AN=146518845&site=eds-live&scope=site
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. https://chamberlainuniversity.idm.oclc.org/login?url=https://search.ebscohost.com/login.aspx?direct=true&db=a9h&AN=146792037&site=eds-live&scope=site