IMPORTANT NOTE REGARDING WORD LIMIT REQUIREMENTS:

Please note that each and every assignment has its own word limit.

Healthy People 2020

Introduction

Hypothesis testing is used to understand the effect of an assumption done on sample data from a larger populace (Donnarumma, Costantini, Ambrosini, Friston & Pezzulo 2017). The test tells the analyst if his central hypothesis is correct or not. Statistical experts test hypotheses through evaluating and examining a random population sample being analyzed. A Z- test is used when comparing two populations mean if they are considerably different from each other or relate if a single community mean, is diverse from a standard value. Currently, we are still working on the objectives of Healthy People 2020. Since according to CDC statistics, over 10% of the US population is diabetic, I opt to work with Diabetes as the topic of choice from the provided website (Centers for Disease Control and Prevention, 2020). The condition cuts across all ages, racial, and cultural groups. It also qualified for this study since the availed data captures from 1980 to 2017, and simple arithmetic will reveal that it gives a sample size with 38 observations (People, 2020). Since that is more than 30, it qualifies to be a large dataset, and would, therefore, fit z-test. In a bid to accurately answer the availed questions on hypothesis testing and understand the selected diabetes data, there is a need to formulate a guiding research question where we will identify the problem and other steps will follow.

Research Question

In every statistical test, there must be a research question that will help in identifying the issue of concern. It is what outlines the researcher’s claim, which gives room for challenging the same to test whether it is wrong or right. The above is known as the significance concept, and it helps in determining whether the researcher employed a quality data source (Gallo, 2016).

Suppose Healthy People 2020 claims that the average diabetes percentage in the country is 7.2, we can test that the average diabetes percentage in the country is different from 7.2 using CDC data from 1980 to 2017, where n= 38, and level of significance is 0.05.

Hypothesis Testing Steps

Problem Identification

Every statistical test starts with problem identification, which comes from the research question. It is the primary issue that the item needs to answer. In the above scenario, for example, the interest parameter is the average diabetes percentage in the country. Identifying the problem helps in narrowing down the specific tests to follow. The focus of this study is to determine whether the average diabetes percentage is 7.2.

Stating Hypotheses

In this section, we have to determine both the null and alternatives hypothesis by incorporating the right signs based on the provided research question.

Step 1: Null hypothesis

By definition, this is the supposition that represents the researcher’s claim. It is the reason why the study holds since we have to confirm if significance, by rejecting or failing to reject it. H₀ is the denotation of the null hypothesis, as shown below (Corty, 2016).

H₀: µ = µ₀ = the researcher’s claim

Similarly, H₁: µ = µ₀ = 7.2

Step 2: Alternatives hypothesis

By definition, this section of the hypothesis is what questions the statistical significance of the researcher’s claims. It provides grounds for rejecting the null theory, based on the sign it employs. It adopts the sign H₁ or H_a (Gallo, 2016). In the above case, we are testing the Healthy People 2020’s claim, which we can summarize as shown below.

H₁: µ ≠ µ₀ ≠ the researcher’s claim

Using the provided scenario, we can rewrite the above as follows;

H₁: µ ≠ 7.2

Step 3: Setting the alpha, ɑ

The standard alpha level is 0.05, and it is the possibility of committing a type 1 error. We also have to note the sample size and level of significance for the test, which is n = 38.

Based on the above two-tailed test, the critical value is given as;

Z critical value, Z_ɑ/2 = Z_0.025 = 1.96.

Step 4: Test Statistics

The next step in hypothesis testing after identifying the appropriate hypothesis is the test statistics. In this case, it is the calculated or empirical z-value defined by the formula below.

Z = (Ȳ- µ) divide by delta over sqrt n,

Where;

Ȳ is the sample mean, µ is the population mean, is the known sample standard deviation, and n is the sample size (Corty, 2016).

We can use the above scenario, from the research question to calculate Z statistics. From the selected sample Ȳ = 5.863, µ = 7.2, while delta = 1.976, and n = 38.

Z = (5.863 – 7.2) divide by 1.976 over sqrt 38 = -4.17

Step 5: The Rejection Region

In simple terms, it is the criteria for rejecting the researcher’s claim, which is the null theory. In making the right criteria, it is vital to understand the tail of the alternative supposition because it helps in the decision-making process. In statistics, we have one and two tail, where one tail is either left or right tail. The next section indicates the rejection procedure based on the type of tail in the alternative theory.

Reject H₀ when Z ≤ – Z_ɑ or when Z ≥ Z_ɑ for left and right tail alternatives, respectively.

Bu reject H₀ when Z ≤ – Z_ɑ/2 or when Z ≥ Z_ɑ/2, for a two tailed test (Corty, 2016).

In the provided scenario, we can demonstrate this, and since our test is two-tailed, we can proceed as follows;

The Z critical value, Z_ɑ/2 = Z_0.025 = 1.96.

We can use the normal distribution to represent the above value and show the rejection region.

Therefore, we compare this with the Z-statics using the above, and reject H₀ if -4.17 ≤ -1.96 or -4.17 ≥ 1.96.

Step 6: Decision-Making and Conclusion

Since it is precise that the Z-statistic value falls in the acceptance region, we would fail to reject H₀ at the 0.05 level of significance (Corty, 2016). It further implies that we are will not reject the claim made by the Healthy People 2020’s report on the average diabetes percentage in the country. It means that, on average, the annual diabetes percentage in the US is 7.2, and it is significant at the 95% level (Gallo, 2016).

Excel Output

The table below shows the z-test for one sample mean for the same data used in the manual calculation of the hypothesis test. While in the above sections, we were indicating a step by step procedure, the output confirms the accuracy of our findings or calculations (Smith, 2016).

z-Test: One-sample for Mean
	Total – Percentage
Mean	5.863157895
Known Variance	3.906174
Observations	38
Hypothesized Mean	7.2
z	-4.169606444
P(Z<=z) one-tail	1.52563E-05
z Critical one-tail	1.644853627
P(Z<=z) two-tail	3.05126E-05
z Critical two-tail	1.959963985

References

American Psychological Association. Publication Manual of the American Psychological Association (6th Ed.). Washington, DC: Author.

Banerjee, A., Karlan, D., & Zinman, J. (2015). Six randomized evaluations of microcredit: Introduction and further steps. American Economic Journal: Applied Economics, 7(1), 1-21.

Centers for Disease Control and Prevention. (2020). National diabetes statistics report, 2020. Atlanta, GA: Centers for Disease Control and Prevention, US Department of Health and Human Services.

Corty, E. W. (2016). Using and interpreting statistics: A practical text for the behavioral, social, and health sciences. Macmillan Higher Education. http://www.gcumedia.com/digital-resources/macmillan-learning/2016/using-and-interpreting-statistics_a-practical-text-for-the-behavioral-social-and-health-sciences_ebook_3e.php

Donnarumma, F., Costantini, M., Ambrosini, E., Friston, K., & Pezzulo, G. (2017). Action perception as hypothesis testing. Cortex, 89, 45-60.

Gallo, A. (2016). A refresher on statistical significance. Harvard Business Review. https://hbr.org/2016/02/a-refresher-on-statistical-significance

People, H. (2020). Annual dental examinations among persons with diagnosed diabetes (age adjusted, percent, 2þ years).

Smith, A., (2016). “Why You Should Love Statistics.” TED website: https://www.ted.com/talks/alan_smith_why_you_should_love_statistics

Your presentation was very impressive. But I got a little lost in the initial problem. My interpretation is that your Health People information indicated that the average A1c for the U.S. is 7.2, or is 7.2 referring to a different variable based on an n=38. Your null hypothesis and alternative hypothesis were valid. I am curious as to why you did not use the standard error method in order to determine the z-value. But if my interpretation is correct pg. 191-192 in our book your value of 4.17 rejects your null hypothesis meaning the healthy data is incorrect.

Respond to the statement above in BOLD based on the three paragraphs ABOVE it… in APA format with At least two references and a minimum of 200 words….. .(The List of References should not be included in the word count.)

• Validate an idea with your own experience.
• Make a suggestion.

Be sure to support your postings and responses with specific references to the Learning Resources.

It is important that you cover all the topics identified in the assignment. Covering the topic does not mean mentioning the topic BUT presenting an explanation from the context of ethics and the readings for this class

To get maximum points you need to follow the requirements listed for this assignments 1) look at the word/page limits 2) review and follow APA rules 3) create subheadings to identify the key sections you are presenting and 4) Free from typographical and sentence construction errors.

REMEMBER IN APA FORMAT JOURNAL TITLES AND VOLUME NUMBERS ARE ITALICIZED.