First, it might not be important, but the title bugs me: statistics isn't a natural science.

I teach economics, and the biggest thing I note about my students is the heterogeneity in mathematical capabilities. I always need to keep on my toes about who I'm boring because they can handle that math in their sleep and who I'm leaving in the dust so that they're not even close to learning what I'm talking about. In a hard science program, there will presumably be some of that, but a bit more pressure on the low end which will make the students more homogeneous.

What to teach depends partly on whether you imagine this is a terminal class for a lot of the students. If so, teach general ideas which they'll be able to dredge up 6 years from now when the ideas are relevant, because they'll forget the details. If it's not a terminal class, try to teach some of the example applications which they might see in future classes.

Behavioral economics is pretty hip these days. Pulling examples from that literature (such as the popular stuff by Dan Ariely) is likely to interest a lot of students and be directly applicable for psychology students (since lots of behavioral economics is more about psychology than economics).

I have a strong bias about how statistics should be taught these days, though I've never tried it and could be proven wrong. I think that statistics should be taught as (1) probability theory, followed by (2) monte carlo methods, and then follow that up with more classical statistics and nonparametric tests. Monte carlo testing gets at the core concepts of what rejecting a null hypothesis means, what confidence is all about, etc and it's straightforward to do these days. Once the ideas are clear, then you could move on to the standard t-tests and so forth. But if you start with monte carlo, the students will grok the notion without knowing calculus as opposed to spending all their time trying to memorize formulas.