Question

A cat-lover claims that cats are just as smart as dogs. In order to back this claim up with some evidence she organizes a study at a large local pet daycare center. A random sample of 40 cats are selected and a random sample of 40 dogs are selected. Each of the selected animals is given one hour with a trainer in which the trainer attempts to teach them to roll over. Upon conclusion of the training, the proportion of dogs and proportion of cats that have learned this skill is computed. The trainer reports that she is 90% confident that the true difference in the proportion of all dogs and all cats (pD – pC) that can learn this skill with one hour of training is between ­–0.05 to 0.28.

Which of the following conclusions can be made based upon this confidence interval?

(A) Because most of the values in the confidence interval are positive, this proves that dogs are smarter than cats
(B) Because the point estimate of the confidence interval is positive, there is convincing evidence that the proportion of all dogs that can learn the skill with one hour of training is greater than the proportion of all cats that can learn the skill with one hour of training.
(C) Because O is contained in the interval, there is not convincing evidence that the proportion of all dogs that can learn the skill with one hour of training differs from the proportion of all cats that can learn the skill with one hour of training.
(D) Because 0.115 is contained in the interval, there is not convincing evidence of a difference in the population proportions.
(E) Because the margin of error of the confidence interval is greater than 0.05, there is not convincing evidence that the proportion of all dogs that can learn the skill with one hour of training differs from the proportion of all cats that can learn the skill with one hour of training.

Answer 1

(C) Because 0 is contained in the interval, there is not convincing evidence that the proportion of all dogs that can learn the skill with one hour of training differs from the proportion of all cats that can learn the skill with one hour of training.

Explanation: