Answer key says out of the choices, the mouse and cow and the least related. Is it because they have the most number of differences out of the four choices? (Hedgehog/Horse is 5, dog/horse is 3, mouse/cow is 7, and mouse/dog is 3). I know there are more complex ways to make the tree, as shown in this video: https://www.youtube.com/watch?v=09eD4A_HxVQ, but I just wanted to know if my logic is correct here. This is for AP biology and we did not learn anything about the technique used in the video. Thank you.
Answer C (Mouse and Cow) is the correct answer to the question, because among the four answer choices, mouse and cow share the earliest common ancestor*.
Under this tree, mouse and cow are more distantly related than the other provided answers because the common ancestor of mouse and cow is deeper in the tree than the common ancestors of the other answer pairs.
However, mouse and cow are not the most distantly related pair across the entire tree. The tree OP constructed*** shows that cow is equally related to each of the four other species. This is because the common ancestor between cow and any other species is the same. Cow/horse are just as distantly-related as cow/mouse, cow/dog, or cow/hedgehog, because each of those pairs diverged at the same point in the tree (with the most recent common ancestor of all five species).
Finally, the algorithm used to construct the tree can make a difference, so it's a little unfair to provide a set of sequences and have someone think up the tree. In this case the question author probably just expected the student to count up the nucleotide differences and select the pair with the most (which most of the time will be the most phylogenetically distant).
*Edit: This originally stated that they were "farthest apart in the tree", but I thought this would lead to confusion with OP's drawing where Cow and Mouse are separated by the greatest horizontal distance in the diagram. To be clear, horizontal distance in the drawing is essentially uninformative to relatedness. One could draw a tree with the same topology as OP's where Cow and Mouse are right next to each other, and it would not change the interpretation.
**I didn't confirm if this is a correct application of that method, but we can assume it is.
***This tree is not accurate to reality. Our best understanding of relationships among these species would put cow sister to horse, who are both sister to dog, who are all sister to hedgehog, who are all sister to mouse. So, basically the exact opposite of this tree. (Although I believe OP correctly constructed their version based on the provided sequences.)