Choosing portable grill displays. Refer to the Journal of Consumer Research (Mar. 2003) experiment on influencing the choices of others by offering undesirable alternatives, presented in Exercise 3.29

(p. 159). Recall that each of 124 college students selected three portable grills out of five to display on the showroom floor. The students were instructed to include Grill #2 (a smaller-sized grill) and select the remaining two grills in the display to maximize purchases of Grill #2. If the six possible grill display combinations (1–2–3, 1–2–4, 1–2–5, 2–3–4, 2–3–5, and 2–4–5) are selected at random, then the proportion of students selecting any display will be 1>6 = .167. One theory tested by the researcher is that the students will tend to choose the three-grill display so that Grill #2 is a compromise between a more desirable and a less desirable grill. Of the 124 students, 85 students selected a three-grill display that was consistent with that theory.

Use this information to test the theory proposed by the researcher at a = .05.

*8.162 Interocular eye pressure. Ophthalmologists require an instrument that can rapidly measure interocular pressure for glaucoma patients. The device now in general use is known to yield readings of this pressure with a variance of 10.3. The variance of five pressure readings on the same eye by a newly developed instrument is equal to 9.8.

Does this sample variance provide sufficient evidence to indicate that the new instrument is more reliable than the instrument currently in use? (Use a = .05.)