Question

26. In a blind side test, do people prefer pate or dog food? To investigate, Bohannon et al. (2010) presented 18 college-educated adults with unlabeled samples of dog food (Newman's Own Organics Canned Turkey and Chicken) and four meat products meant for humans (duck liver mousse, pork liver pate, livewurst, and Spam). Participants were asked to rank their preferences. Two of 18 participants ranked the dog food first, whereas the other 16 participants chose one of the other items. Based on these results, can we conclude that people are less likely to prefer dog food over all human food than would be expected by chance?

Answer 1

here if both food are equally likely then

this is binomial with parameter n=18 and p=2/6 =1/3

P(at 2 or less people out of 18 like dog food) :

P(X<=2)=P(X=0)+P(X=1)+P(X=2) =

∑x=02     (18Cx)(1/3)x(2/3)(18-x)    =

0.0326

since the probability of this event is significantly low (less than 0.05) ,

we can conclude that people are less likely to prefer dog food over all human food than would be expected by chance