For this exercise, refer to the explanation and data for Exercise 11.85 about goats' response to social cues.
a. Use software to carry out a two-sample test for a significant difference between scores of adults and juveniles when cued with gazing. First report the sample mean scores and tell which is higher.
b. Report the P-value.
c. Using a 0.05 as your cut-off for a small P-value, state whether or not the data provide convincing evidence of a difference.
d. Suppose that researchers already had reason to believe that juveniles perform better than adults when cued with gazing. What would the P-value be in this case?
e. Use a 0.05 as your cut-off for a small P-value, and state whether or not the data provide convincing evidence that juveniles' mean is higher.
f. Suppose that researchers already had reason to believe that adults perform better than juveniles when cued with gazing. Do the data provide evidence that this is the case? Explain.
Exercise 85
Researchers at the Max Planck Institute for Evolutionary Anthropology in Germany experimented on goats' ability to follow certain social cues, with results published in the online journal Animal Behavior in January 2005. "We tested goats' ability to use gaze and other communicative cues given by a human in a so-called object choice situation. An experimenter hid food out of sight of the subject under one of two cups. After baiting the cup the experimenter indicated the location of the food to the subject by using different cues [touching, pointing, gazing, or none for control]."37 This table shows scores for 13 adult and 10 juvenile goats when given the various cues, where the maximum possible score each time was 18.
a. For the adult goats, find the sample mean scores for gaze and control. Explain why a formal test is not necessary to draw this conclusion: The adult goats did not perform significantly better when cued with a gaze than they did with no cue (control).
b. Use software to carry out a paired test to see if the juvenile goats performed significantly better when cued with a gaze than they did with no cue. Report the mean of differences (gaze minus control), the standardized mean of differences (t), and the P-value, and state your conclusions.
c. If the mean of differences in part (b) had been negative, what would this tell us about performance when cued with a gaze compared to no cue at all, for the sample of juvenile goats?
d. Another way of determining whether or not juvenile goats respond to cues of gazing is to compare their mean gaze score to 9, which should be the overall mean if gazing does not help the goats in the 18 cup-selection tasks. Carry out a test to see if their mean score was significantly higher than 9; are our conclusions consistent with those of part (b)?