Chapter 11.2, Problem 26E

The article “Puppy Love? It’s Real, Study Says” (USA TODAY, April 17, 2015) describes a study into how people communicate with their pets. The conclusion expressed in the title of the article was based on research published in Science (“Oxytocin-Gaze Positive Loop and the Coevolution of Human-Dog Bonds,” April 17, 2015). Researchers measured the oxytocin levels (in picograms per milligram, pg/mg) of 22 dog owners before and again after a 30-minute interaction with their dogs. (Oxytocin is a hormone known to play a role in parent-child bonding.) The difference in oxytocin level (before – after) was calculated for each of the 22 dog owners. Suppose that the mean and standard deviation of the differences (approximate values based on a graph in the paper) were ${\bar{x}}_d$ = 27 pg/mg and s_d = 30 pg/mg.

1. a. Explain why the two samples (oxytocin levels before interaction and oxytocin levels after interaction) are paired.
2. b. Assume that it is reasonable to regard the 22 dog owners who participated in this study as representative of dog owners in general. Do the data from this study provide convincing evidence that there is an increase in mean oxytocin level of dog owners after 30 minutes of interaction with their dogs? State and test the appropriate hypotheses using a significance level of 0.05.