A team of researchers wants to determine whether pet owners are generally more satisfied with their lives than non-pet owners. To test their theory, the researchers randomly select 500 pet owners and 500 non-pet owners from several major metropolitan areas in the country. The researchers then interview the individuals, asking them a series of questions. Each response is assessed with a point value that is later translated to a satisfaction indicator. Of the pet owners surveyed, 380 of the 500 were found to be satisfied with their lives, while 336 of the 500 non-pet owners were found to be satisfied.
A. Would this study be considered an experiment or an observational study? Explain.
B. Say that the researchers decide to run a z-test for the difference of two proportions to see if a higher proportion of pet owners are satisfied with their lives than non-pet owners. What would be the null and alternative hypotheses tested? Be sure to identify the parameters being tested.
C. What conditions must be checked in order to perform this test? Comment on whether or not each condition is satisfied.
D. The p-value for the test against the alternative hypothesis, which states that a higher proportion of pet owners are satisfied with their lives than non-pet owners, is 0.0010. Interpret this p-value.