For this exercise, refer to the explanation and data for Exercise 11.85 about goats' response to social cues.
a. If researchers want to construct a confidence interval to see how much better juvenile goats perform when cued with touching compared to pointing, is this a paired or two-sample design?
b. Use software to produce the interval described in part (a).
c. Does the interval that you reported in part (b) clearly contain zero, or just barely, or not quite, or not at all?
d. Use your answer to part (c) to tell whether you expect the null hypothesis of no difference between touching and pointing to be rejected, or not rejected, or if results may be borderline.
e. If researchers want to construct a confidence interval to see how much better juvenile goats perform compared to adults when cued with touching, is this a paired or two-sample design?
f. Use software to produce the interval described in part (e).
g. Does the interval you reported in part (f) contain zero clearly, just barely, not quite, or not at all?
h. Use your answer to part (g) to tell whether or not you expect the null hypothesis of no difference between juveniles and adults to be rejected, or if results may be borderline.
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)?