Can a hawk carry off a 4lb hen?

We had problems with hawks late fall, but nothing since then. I let me chickens out completely free range, so I expect to lose a few. I have been getting more "flighty" breeds, and they seem to do really well looking out for and avoiding predators. This week, though, we lost one of my dh and kids' favorite hens, a salmon Faverolles. She was very small, though, only about 4 lbs, maybe a little less. She was in the bantam bin, but ended up somewhere between bantam and standard size. Honestly, I am not very uspet about her. We've had someone pecking eggs the last month or so, and I caught her in the act last week. We had at least 4 eggs a day get pecked. Since she disappeared, we've had none. She was going to disappear soon anyway, and I am sort of relieved I didn't have to do it since my dh and kids loved her so much. We also lost a little Pekin duckling and a 3 month old mixed breed pullet. All in the last week. Absolutely no sign of anything. We have a puppy, 3 mos old, and our goats seem to be keeping the coons and possums away. I think if the puppy had done it, there would be bodies strewn about. She chases everything, but I have never seen her hurt any. I'm working on her, but she's only 3 mos old.

I did find a spot under a large oak that had a lot of feathers under it. It's hard to tell if they landed there or the wind blew them there, it's been very windy. Sound like a hawk? Or are the smaller predators not as afraid of my goats as I've been assuming? We also have a lot of stray cats around. I doubt one of those could have taken my 4lb hen, but they certainly could be to blame for the 3 mo old bantam pullet and the 3 week old duckling. I sort of suspect hawk for all 3 though. We have a whole family of redtails that nests in a neighbor's yard.

It was a fox. My kids saw it in the pen this morning. Chickens were still locked up for the night. But if it is coming during the day, then that is where our missing chickens went. They said the goats were all 3 standing up on the milking stand (2 mamas, 1 baby.)  I am surprised b/c they will chase dogs away. Apparently they are more afraid of a fox than a dog and know the difference. Since the chickens spend a lot of time in the goat pen, the fox was def there for chicken, just too early in the day. :( I think I'm going to spend some time down there with a gun. If it is getting into the goat pen and my chickens can get in there, there is not much else I can do. The pen is way too big to chicken proof. The neighbors had told me about the fox last fall, said it had killed small pets in the past, but this is the first sign of it I've seen.

My puppy is not outside totally unsupervised. But she does run around while I am feeding and watering, so there are times when I am out there with her but not watching her. If she were killing my chickens, I would certainly hear something and see some evidence. She's a herder, so she does a LOT of chasing, but I've never seen her bite a chicken other than nipping at its tail. They run from her, but they don't even make alarm calls, so they aren't all that afraid of her.

My friend was here late. her son came back into the house when they were leaving for something he forgot and left the door wide open when he left. I thought I heard her go out when he left and she didn't come when I call her, so I knew something was up. The look on her face is priceless. "I'm sorry, mommy! Don't be mad!"