Week 7 Discussion: Rejection Region
The data set I choose for this week’ s discussion is on prevalence of diagnosed and undiagnosed (total) diabetes among U.S. adults aged 18 years and older in the years 1999-2016. The dataset is taken from National Diabetes Statistics Report 2020 by Centers for Disease Control and Prevention.

Years

% of U.S. adults 18 years and older with diagnosed and undiagnosed diabetes

1999-2002

9.5%

2001-2004

10.3%

2003-2006

10.2%

2005-2008

10.6%

2007-2010

11.1%

2009-2012

11.3%

2011-2014

11.5%

2013-2016

12.0%

In this data, I observe that the prevalence of diabetes significantly increased among adults age 18 years and older in the U.S. Based on the dataset, I claim that at least 12.0 % of the U.S adult population of 18 years and older have diabetes.

To test my claim, I would perform a hypothesis testing. According to Chamberlain College of Nursing (2020), the first step in hypothesis testing is to identify the null hypothesis and the alternative hypothesis. The null hypothesis is the statistical hypothesis that contains a statement of equality with symbols either greater/less than or equal to or equal to. In this case my null hypothesis be H0: P . (greater or equal to). That is my claim. The alternative hypothesis is the compliment of the null hypothesis. Therefore, it does not contain the equality symbols. The alternative hypothesis for my claim is that Ha: P 0.12. Then, the next step is to determine what kind of test is to run based on the alternative hypothesis. If the alternative hypothesis contains less than symbol like the one in my example claim, the test is the left-tailed test. Thus, my test is left-tailed.

The steps needed to complete the hypothesis test depends on the given data. For example, the steps in hypothesis testing for population proportion include

1. Verify that the sampling distribution of p hat can be approximated by a normal distribution. (which means verifying np 5 and nq5)

2. Identify the null and alternative hypothesis.

3. Determine level of significance.

4. Determine the critical value using a z-table.

5. Draw a normal distribution graph and determine the rejection zone(s).

6. Find the standardized test statistic and sketch the sampling distribution

7. Make a decision to reject or fail to reject hypothesis. (Chamberlain College of nursing, 2020).

We are looking for an average percentage here.

Hyp-5.jpg

The sample size is 8.

Pease can you continue from here?