Where do you look when you are listening to someone speak? Researchers have discovered that listeners tend to gaze at the eyes or mouth of the speaker. In a study published in Perception & Psychophysics (Aug. 1998), subjects watched a videotape of a speaker giving a series of short monologues at a social gathering (e.g., a party). The level of background noise (multilingual voices and music) was varied during the listening sessions. Each subject wore a pair of clear plastic goggles on which an infrared corneal detection system was mounted, enabling the researchers to monitor the subject’s eye movements. One response variable of interest was the proportion y of times the subject’s eyes fixated on the speaker’s mouth.

a. The researchers wanted to estimate E(y) for four different noise levels: none, low, medium, and high. Hypothesize a model that will allow the researchers to obtain these estimates.

b. Interpret the β’s in the model you hypothesized in part a.

c. Explain how to test the hypothesis of no differences in the mean proportions of mouth fixations for the four background noise levels.