Psychology researchers from the University of California, San Diego, set about finding an answer to the question, "Do dogs resemble their owners?" In their study, "28 student judges were asked to match photos of dogs with their owners. Each student was presented with a photo of a dog owner and photos of two dogs; one dog was the actual pet, the other was an imposter. If more than half of the judges correctly paired a given dog with his or her owner, this was considered a "match." Forty-five dogs took part in the study-25 purebreds and 20 mutts. [. . .] Overall, there were just 23 matches (as defined above). However, the judges had an easier time with the purebred dogs: 16 matches, versus 7 for the mixed breeds."9
a. Overall, what proportion of the 45 dogs were correctly matched with their owners?
b. Of the 25 purebreds, what proportion were correctly matched with the dogs' owners?
c. Suppose only 3 dogs were included in the study. Would it be common, or would it be unusual, for at least two-thirds to be matched correctly, purely by chance?
d. Your answer to part (b) indicates that a clear majority in the sample were able to match correctly for the purebred dogs. If this proportion were being used as evidence that, in general, people can match purebred dogs to their owners, would it be more convincing, less convincing, or equally convincing if it arose from a sample of 250 dogs instead of 25?