11.77 Here’s one to sink your teeth into: The authors of the article “Analysis of Food Crushing Sounds During Mastication: Total Sound Level Studies” (Journal of Texture Studies [1990]: 165– 178) studied the nature of sounds generated during eating. Peak loudness (in decibels at 20 cm away) was measured for both open-mouth and closed-mouth chewing of potato chips and of tortilla chips. Forty subjects participated, with ten assigned at random to each combination of conditions (such as closed-mouth potato chip, and so on). We are not making this up! Summary values taken from plots given in the article appear in the accompanying table. For purposes of this exercise, suppose that it is reasonable to regard the peak loudness distributions as approximately normal.

n x s Potato Chip Open mouth 10 63 13 Closed mouth 10 54 16 Tortilla Chip Open mouth 10 60 15 Closed mouth 10 53 16

a. Construct a 95% confidence interval for the difference in mean peak loudness between open-mouth and closed-mouth chewing of potato chips. Interpret the resulting interval.

b. For closed-mouth chewing (the recommended method!), is there sufficient evidence to indicate that there is a difference between potato chips and tortilla chips with respect to mean peak loudness? Test the relevant hypotheses using a  .01.

c. The means and standard deviations given here were actually for stale chips. When ten measurements of peak loudness were recorded for closed-mouth chewing of fresh tortilla chips, the resulting mean and standard deviation were 56 and 14, respectively. Is there sufficient evidence to conclude that fresh tortilla chips are louder than stale chips? Use a  .05.