"Domestic Goats Follow Gaze Direction and Use Social Cues in An Object Choice Task," published online in Animal Behavior in January 2005, included information on 23 goats' performance in a bucket-selection task, when cued in one of two ways. The mean score when cued by a handler touching the correct bucket was 14.3; the mean score when cued by pointing was 11.4. Both standard deviations are the same.
a. If the goats perform at chance level, they would average 9 overall. Which standardized sample mean would be higher: the one for touching or the one for pointing?
b. Explain why your answer to part (a) would not necessarily be correct if the standard deviations differed.
c. Explain why your answer to part (a) would not necessarily be correct if the sample sizes differed.
d. Which P-value would be smaller: the one for touching or the one for pointing?
e. The standardized test statistic for pointing, which follows an approximate z distribution, is 5.4. Did the goats perform significantly better than chance when cued by touching, pointing, both, or neither?