HYPOTHESIS TESTING

Suppose that a 2012 National Health Interview Survey gives the number of adults in the United States (reported in thousands), classified by their age group, and whether or not respondents have ever been tested for HIV. Here is the data:

Age Group	Tested (T)	Never Tested (NT)
18-44 years	50,080	56,405
45-64 years	23,768	48,537
65-74 years	2,694	15,162
75 years and older	1,247	14,663
Total	77,789	134,767

1. Define probability. What is its history? Describe the theory of probability. How is it calculated? What are the advantages and disadvantages of using probability?
2. Identify and discuss the two major categories of probability interpretation, and how the two interpretations possess conflicting views about the fundamental nature of probability.
3. Based on this survey, what is the probability that a randomly selected American adult has never been tested? Show your work. Hint: using the data in the two total rows, this would be calculated as p (NT) /( p (NT) + p (T)), where p is probability.
4. What proportion of 18- to 44-year-old Americans has never been tested for HIV? Hint: using the values in the 18-44 cells, this would be calculated as p (NT) / ( p (NT) + p (T)), where p is probability. Show your work.