Samuel recently got his first dog, and he's considering if he should pay for professional dog training. He's skeptical paying for this training is worth it, but fortunately Samuel is a statistician and friends with some researchers at the veterinary school. They randomly recruit 70 dogs to take part in the study, and a respected pet trainer in the region agrees to help train these dogs as part of the study.

Prior to the study, Samuel and the vets pair off all the dogs based on both biological characteristics as well as owner characteristics. As a result, they have 35 pairs of dogs that are relatively similar. One dog in each pair is randomly chosen to receive the professional behavior training, while the other dog will not receive the training (but will still be trained by its owners).

After training the dogs for two months, a second professional dog trainer is brought in to assess the obedience levels of all the dogs. Assume they are able to do so and can convert their ratings to a 0-100 point scale (treat this as being quantitative and not categorical). A 100 is a perfectly obedient dog. The second dog trainer does not know which dog received the treatment and which received the control.

Histograms for each of the three rows of data indicates that they are reasonably close to being normally distributed.

Calculate the appropriate test statistic to test the hypothesisH0 : ?D = 0 HA : ?D > 0

?dis the true mean difference in obedience score a dog would receive if they were professionally trained instead of being solely trained by its owners. Give your answer to two digits past the decimal point.

Professionally Pair 1 Pair 2 Pair 35 Mean St Dev trained? No 88 56 34 62.1 11.3 Yes 97 52 47 70.4 14.1 Diff (yes - no) 9 -4 13 8.3 4.02