It's the Socialist Worker's quiz, so they'd like to convince you that the answer is "yes." But they had to admit that, for me, the answer is "no."
There's a weird throwaway question about the US military being a force for good in the world, which of course it is -- but that's not really a socialism issue, is it? I wondered if it might be a trick question, since some people sometimes argue that the military is the most socialist part of the United States. (It's not a very good argument.)
Partly the problem is that the quiz runs things together that don't belong together. Do I think that schools, clean water, and hospitals should never be run for profit? Well, no; but I also think that there's a huge difference between "schools," "hospitals," and "clean water." To me, that's not a category of things that should be run for the common good instead of private interest; it's an ascending scale. I don't think I'd ever be annoyed at someone for starting a private school, even if they charged a fortune for attendance. We've just seen an argument from Tex that it can make really good sense to run a private hospital business alongside a public one. Even if we agree that we should provide some sort of public access to health care, that doesn't imply that every hospital should be nonprofit.
There are several things about water that make it a stronger case for a public approach. In a city, the infrastructure concerns are going to mean that you'll almost certainly get a monopoly, and monopolies are problematic. We often address them with public regulation. Too, even in rural areas where people have wells, the nature of water means that the water table under your house is the same one your neighbor is pulling from. Let's say that you had a neighbor who came in, dug a well, and began bottling and selling the water to such a degree that everyone began having trouble getting water. Your wells might even go dry, but he can dig a deeper one with the profits from the water he sold after sucking it out of the same water table you were using. When dealing with these kinds of issues, at least some democratic controls on the market activity often make good sense.