4.12 Psychology researchers from the University uld tter of California, San Dieg

Question

4.12 Psychology researchers from the University uld tter 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 is to ries or lo in , or were correctly matched with their owners? b. Of the 25 purebreds, what proportion 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?

Explanation / Answer

(a) Total number of dogs which were to be matched = 45

Number of dogs correctly matched = 23

Proportion of dogs correctly matched = 23/45 = 0.511

Percentage of dogs correctly matched = 51.11%

(b) There were 25 purebreds and 16 were matched.

So the proportion of the purebreds corerctly matched = 16/25 = 0.64

This is 64% of the number of purebreds which were matched.

(c) We see that the overall proportion of dogs matched = 0.51 and this proportion is 0.64 for purebreds.

So it would be unusual for two-thirds (a proportion of 0.75) of the dogs to be matched purely by chance.

(d) It would be more convincing if the results arose from a sample of 250 dogs instead of 25, because a larger sample size leads to more accurate representation of the population under study.

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