Chapter 8.4, Problem 1TY

Consider the results of the study discussed on page 417. At α = 0.05, can you support the claim that there is a difference between the proportion of yoga users who are 40- to 49-year-olds and the proportion of non-yoga users who are 40- to 49-year-olds?

Answer: Page A37

In Chapter 6, you were introduced to inferential statistics and you learned how to form a confidence interval to estimate a population parameter. Then, in Chapter 7, you learned how to test a claim about a population parameter, basing your decision on sample statistics and their sampling distributions.

Using data from the National Health Interview Survey, a study was conducted to analyze the characteristics of yoga users and non-yoga users. The study was published in the Journal of General Internal Medicine. Some of the results are shown below for a random sample of yoga users.

Yoga Users (n = 1593)
Characteristic	Frequency	Proportion
40 to 49 years old	367	0,2304
Income of $20,000 to S34,999	239	0,1500
Non-smoking	1323	0,8305

In this chapter, you will continue your study of inferential statistics and hypothesis testing. Now, however, instead of testing a hypothesis about a single population, you will learn how to test a hypothesis that compares two populations.

For instance, in the yoga study, a random sample of non-yoga users was also surveyed. Here are the study’s findings for this second group.

Non-Yoga Users (n = 29,948)
Characteristic	Frequency	Proportion
40 to 49 years old	6,290	0,2100
Income of $20,000 to $34,999	5,990	0,2000
Non-smoking	23,360	0,7800

From these two samples, can you conclude that there is a difference in the proportion of 40- to 49-year-olds, people with an income of $20,000 to $34,999, or non-smokers between yoga users and non-yoga users? Or, might the differences in the proportions be due to chance?

In this chapter, you will learn to answer these questions by testing the hypothesis that the two proportions are equal. For instance, for non-smokers, you can conclude that the proportion of yoga users is different from the proportion of non-yoga users.