A 2009 Study to Investigate the Dominant Paws in Cats

A 2009 study to investigate the dominant paws in cats was described in Animal Behaviour (Volume 78, Issue 2). The researchers used a random sample of 42 domestic cats. In this study, each cat was shown a treat (5 grams of tuna), and while the cat watched, the food was placed inside a jar. The opening of the jar was small enough that the cat could not stick its head inside to remove the treat. The researcher recorded the paw that was first used by the cat to try to retrieve the treat. This was repeated 100 times for each cat (over a span of several days). The paw used most often was deemed the dominant paw (note that one cat used both paws equally and was classified as "ambidextrous"). The researchers were also interested in comparing the proportion of "left-pawed"
cats for male and female cats. Of the 21 male cats in the sample, 19 were classified as "left-pawed"
while only 1 of the 21 female cats were considered to be "left-pawed". Explain why it would not be appropriate to use the normal distribution to construct a confidence interval for the difference in the proportion of male and female cats that are "left-pawed".